Tamil Nadu Board of Secondary EducationHSC Science Class 11th
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Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 8 - Vector Algebra [Latest edition]

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Class 11th Mathematics Volume 1 and 2 Answers Guide - Shaalaa.com
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Chapter 8: Vector Algebra

Exercise 8.1Exercise 8.2Exercise 8.3Exercise 8.4Exercise 8.5
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Exercise 8.1 [Pages 59 - 60]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 8 Vector AlgebraExercise 8.1 [Pages 59 - 60]

Exercise 8.1 | Q 1. (i) | Page 59

Represent graphically the displacement of 45 cm, 30° north of east

Exercise 8.1 | Q 1. (ii) | Page 59

Represent graphically the displacement of 80 km, 60° south of west

Exercise 8.1 | Q 2 | Page 59

Prove that the relation R defined on the set V of all vectors by `vec"a"  "R"  vec"b"`  if  `vec"a" = vec"b"` is an equivalence relation on V

Exercise 8.1 | Q 3 | Page 59

Let `vec"a"` and `vec"b"` be the position vectors of the points A and B. Prove that the position vectors of the points which trisects the line segment AB are `(vec"a" + 2vec"b")/3` and `(vec"b" + 2vec"a")/3`

Exercise 8.1 | Q 4 | Page 60

If D and E are the midpoints of the sides AB and AC of a triangle ABC, prove that `vec"BE" + vec"DC" = 3/2vec"BC"`

Exercise 8.1 | Q 5 | Page 60

Prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third side whose length is half of the length of the third side

Exercise 8.1 | Q 6 | Page 60

Prove that the line segments joining the midpoints of the adjacent sides of a quadrilateral form a parallelogram

Exercise 8.1 | Q 7 | Page 60

If `vec"a"` and `vec"b"` represent a side and a diagonal of a parallelogram, find the other sides and the other diagonal

Exercise 8.1 | Q 8 | Page 60

If `vec"PO" + vec"OQ" = vec"QO" + vec"OR"`, prove that the points P, Q, R are collinear

Exercise 8.1 | Q 9 | Page 60

If D is the midpoint of the aide BC of a triangle ABC, prove that `vec"AB" + vec"AC" = 2vec"AD"`

Exercise 8.1 | Q 10 | Page 60

If G is the centroid of a triangle ABC, prove that `vec"GA" + vec"GB" + vec"GC" = vec0`

Exercise 8.1 | Q 11 | Page 60

Let A, B, and C be the vertices of a triangle. Let D, E, and F be the midpoints of the sides BC, CA, and AB respectively. Show that `vec"AD" + vec"BE" + vec"CF" = vec0`

Exercise 8.1 | Q 12 | Page 60

If ABCD is a quadrilateral and E and F are the midpoints of AC and BD respectively, then Prove that `vec"AB" + vec"AD" + vec"CB" + vec"CD" = 4vec"EF"`

Exercise 8.2 [Pages 60 - 68]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 8 Vector AlgebraExercise 8.2 [Pages 60 - 68]

Exercise 8.2 | Q 1. (i) | Page 68

Verify whether the following ratios are direction cosines of some vector or not

`1/5, 3/5, 4/5`

Exercise 8.2 | Q 1. (ii) | Page 68

Verify whether the following ratios are direction cosines of some vector or not

`1/sqrt(2), 1/2, 1/2`

Exercise 8.2 | Q 1. (iii) | Page 68

Verify whether the following ratios are direction cosines of some vector or not

`4/3, 0, 3/4`

Exercise 8.2 | Q 2. (i) | Page 68

Find the direction cosines of a vector whose direction ratios are
1, 2, 3

Exercise 8.2 | Q 2. (ii) | Page 60

Find the direction cosines of a vector whose direction ratios are

`1/sqrt(2), 1/2, 1/2`

Exercise 8.2 | Q 2. (iii) | Page 68

Find the direction cosines of a vector whose direction ratios are
0, 0, 7

Exercise 8.2 | Q 3. (i) | Page 68

Find the direction cosines and direction ratios for the following vector

`3hat"i" - 4hat"j" + 8hat"k"`

Exercise 8.2 | Q 3. (ii) | Page 68

Find the direction cosines and direction ratios for the following vector

`3hat"i" + hat"j" + hat"k"`

Exercise 8.2 | Q 3. (iii) | Page 68

Find the direction cosines and direction ratios for the following vector

`hat"j"`

Exercise 8.2 | Q 3. (iv) | Page 68

Find the direction cosines and direction ratios for the following vector

`5hat"i" - 3hat"j" - 48hat"k"`

Exercise 8.2 | Q 3. (v) | Page 68

Find the direction cosines and direction ratios for the following vector

`3hat"i" - 3hat"k" + 4hat"j"`

Exercise 8.2 | Q 3. (vi) | Page 68

Find the direction cosines and direction ratios for the following vector

`hat"i" - hat"k"`

Exercise 8.2 | Q 4 | Page 68

A triangle is formed by joining the points (1, 0, 0), (0, 1, 0) and (0, 0, 1). Find the direction cosines of the medians

Exercise 8.2 | Q 5 | Page 68

If `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a

Exercise 8.2 | Q 6 | Page 68

If (a, a + b, a + b + c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0), then find a set of values of a, b, c

Exercise 8.2 | Q 7 | Page 68

Show that the vectors `- 2hat"i" - hat"j" - hat"k", - 3hat"i" - 4hat"j" - 4hat"k", hat"i" - 3hat"j" - 5hat"k"` form a right angled triangle

Exercise 8.2 | Q 8 | Page 68

Find the value of λ for which the vectors `vec"a" = 3hat"i" + 2hat"j" + 9hat"k"` and `hat"b" = hat"i" + lambdahat"j" + 3hat"k"` are parallel

Exercise 8.2 | Q 9. (i) | Page 68

Show that the following vectors are coplanar

`hat"i" - 2hat"j" + 3hat"k", -2hat"i" + 3hat"j" - 4hat"k", -hat"j" + 2hat"k"`

Exercise 8.2 | Q 9. (ii) | Page 68

Show that the following vectors are coplanar

`2hat"i" + 3hat"j" + hat"k", hat"i" - hat"j", 7hat"i" + 3hat"j" + 2hat"k"`

Exercise 8.2 | Q 10 | Page 68

Show that the points whose position vectors `4hat"i" + 5hat"j" - hat"k", - hat"j" - hat"k", 3hat"i" + 9hat"j" + 4hat"k"` and `-4hat"i" + 4hat"j" + 4hat"k"` are coplanar

Exercise 8.2 | Q 11. (i) | Page 68

If `vec"a" = 2hat"i" + 3hat"j" - 4hat"k", vec"b" = 3hat"i" - 4hat"j" - 5hat"k"`, and `vec"c" = -3hat"i" + 2hat"j" + 3hat"k"`,  find the magnitude and direction cosines of `vec"a", vec"b", vec"c"`

Exercise 8.2 | Q 11. (ii) | Page 68

If `vec"a" = 2hat"i" + 3hat"j" - 4hat"k", vec"b" = 3hat"i" - 4hat"j" - 5hat"k"`, and `vec"c" = -3hat"i" + 2hat"j" + 3hat"k"`,  find the magnitude and direction cosines of `3vec"a"- 2vec"b"+ 5vec"c"`

Exercise 8.2 | Q 12 | Page 68

The position vectors of the vertices of a triangle are `hat"i" + 2hat"j" + 3hat"k", 3hat"i" - 4hat"j" + 5hat"k"` and `-2hat"i" + 3hat"j" - 7hat"k"`. Find the perimeter of the triangle

Exercise 8.2 | Q 13 | Page 68

Find the unit vector parallel to `3vec"a" - 2vec"b" + 4vec"C"` if `vec"a" = 3hat"i" - hat"j" - 4hat"k", vec"b" = -2hat"i" + 4hat"j" - 3hat"k"`, and `vec"c" = hat"i" + 2hat"j" - hat"k"`

Exercise 8.2 | Q 14 | Page 68

The position vectors `vec"a", vec"b", vec"c"` of three points satisfy the relation `2vec"a" - 7vec"b" + 5vec"c" = vec0`. Are these points collinear?

Exercise 8.2 | Q 15 | Page 68

The position vectors of the points P, Q, R, S are `hat"i" + hat"j" + hat"k", 2hat"i" + 5hat"j", 3hat"i" + 2hat"j" - 3hat"k"`, and `hat"i" - 6hat"j" - hat"k"` respectively. Prove that the line PQ and RS are parallel

Exercise 8.2 | Q 16 | Page 68

Find the value or values of m for which `"m"(hat"i" + hat"j" + hat"k")` is a unit vector

Exercise 8.2 | Q 17 | Page 68

Show that the points A(1, 1, 1), B(1, 2, 3) and C(2, – 1, 1) are vertices of an isosceles triangle

Exercise 8.3 [Page 74]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 8 Vector AlgebraExercise 8.3 [Page 74]

Exercise 8.3 | Q 1. (i) | Page 74

Find `vec"a"*vec"b"` when `vec"a" = hat"i" - 2hat"j" + hat"k"` and `vec"b" = 3hat"i" - 4hat"j" - 2hat"k"`

Exercise 8.3 | Q 1. (ii) | Page 74

Find `vec"a"*vec"b"` when `vec"a" = 2hat"i" + 2hat"j" - hat"k"` and `vec"b" = 6hat"i" - 3hat"j" + 2hat"k"`

Exercise 8.3 | Q 2. (i) | Page 74

Find the value λ for which the vectors `vec"a"` and  `vec"b"` are perpendicular, where `vec"a" = 2hat"i" + lambdahat"j" + hat"k"` and `vec"b" = hat"i" - 2hat"j" + 3hat"k"`

Exercise 8.3 | Q 2. (ii) | Page 74

Find the value λ for which the vectors `vec"a"` and `vec"b"` are perpendicular, where `vec"a" = 2hat"i" + 4hat"j" - hat"k"` and `vec"b" = 3hat"i" - 2hat"j" + lambdahat"k"`

Exercise 8.3 | Q 3 | Page 74

If `vec"a"` and `vec"b"` are two vectors such that `|vec"a"| = 10, |vec"b"| = 15` and `vec"a"*vec"b" = 75sqrt(2)`, find the angle between `vec"a"` and `vec"b"`

Exercise 8.3 | Q 4. (i) | Page 74

Find the angle between the vectors

`2hat"i" + 3hat"j" - 6hat"k"` and `6hat"i" - 3hat"j" + 2hat"k"`

Exercise 8.3 | Q 4. (ii) | Page 74

Find the angle between the vectors

`hat"i" - hat"j"` and `hat"j" - hat"k"`

Exercise 8.3 | Q 5 | Page 74

If `vec"a", vec"b", vec"c"` are three vectors such that `vec"a" + 2vec"b" + vec"c"` = 0 and `|vec"a"| = 3, |vec"b"| = 4, |vec"c"| = 7`, find the angle between `vec"a"` and `vec"b"`

Exercise 8.3 | Q 6 | Page 74

Show that the vectors `vec"a" = 2hat"i" + 3hat"j" + 3hat"j" + 6hat"k", vec"b" = 6hat"i" + 2hat"j" - 3hat"k"` and `vec"c" = 3hat"i" - 6hat"j" + 6hat"k"` are mutually orthogonal

Exercise 8.3 | Q 7 | Page 74

Show that the vectors `-hat"i" - 2hat"j" - 6hat"k", 2hat"i" - hat"j" + hat"k"` and find `-hat"i" + 3hat"j" + 5hat"k"` form a right angled triangle

Exercise 8.3 | Q 8 | Page 74

If `|vec"a"|= 5, |vec"b"| = 6, |vec"c"| = 7` and `vec"a" + vec"b" + vec"c" = vec"0"`, find `vec"a" * vec"b" + vec"b" *vec"c" + vec"c" * vec"a"`

Exercise 8.3 | Q 9 | Page 74

Show that the points (2, –1, 3), (4, 3, 1) and (3, 1, 2) are collinear

Exercise 8.3 | Q 10. (i) | Page 74

If `vec"a", vec"b"` are unit vectors and q is the angle between them, show that 

`sin  theta/2 = 1/2|vec"a" - vec"b"|`

Exercise 8.3 | Q 10. (ii) | Page 74

If `vec"a", vec"b"` are unit vectors and q is the angle between them, show that 

`cos  theta/2 = 1/2|vec"a" + vec"b"|`

Exercise 8.3 | Q 10. (iii) | Page 74

If `vec"a", vec"b"` are unit vectors and q is the angle between them, show that 

`tan  theta/2 = |vec"a" - vec"b"|/|vec"a" + vec"b"|`

Exercise 8.3 | Q 11 | Page 74

Let `vec"a", vec"b", vec"c"` be three vectors such that `|vec"a"| = 3, |vec"b"| = 4, |vec"c"| = 5` and each one of them being perpendicular to the sum of the other two, find `|vec"a" + vec"b" + vec"c"|`

Exercise 8.3 | Q 12 | Page 74

Find the projection of the vector `hat"i" + 3hat"j" + 7hat"k"` on the vector `2hat"i" + 6hat"j" + 3hat"k"`

Exercise 8.3 | Q 13 | Page 74

Find λ, when the projection of `vec"a" = lambdahat"i" + hat"j" + 4hat"k"` on `vec"b" = 2hat"i" + 6hat"j" + 3hat"k"` is 4 units

Exercise 8.3 | Q 14 | Page 74

Three vectors `vec"a", vec"b"` and `vec"c"` are such that `|vec"a"| = 2, |vec"b"| = 3, |vec"c"| = 4`, and `vec"a" + vec"b" + vec"c" = vec0`. Find `4vec"a"*vec"b" + 3vec"b"*vec"c" + 3vec"c"*vec"a"`

Exercise 8.4 [Pages 79 - 80]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 8 Vector AlgebraExercise 8.4 [Pages 79 - 80]

Exercise 8.4 | Q 1 | Page 79

Find the magnitude of `vec"a" xx vec"b"` if `vec"a" = 2hat"i" + hat"j" + 3hat"k"` and `vec"b" = 3hat"i" + 5hat"j" - 2hat"k"`

Exercise 8.4 | Q 2 | Page 79

Show that `vec"a" xx (vec"b" + vec"c") + vec"b" xx (vec"c" + vec"a") + vec"c" xx (vec"a" + vec"b") = vec0`

Exercise 8.4 | Q 3 | Page 79

Find the vectors of magnitude `10sqrt(3)` that are perpendicular to the plane which contains `hat"i" + 2hat"j" + hat"k"` and `hat"i" + 3hat"j" + 4hat"k"`

Exercise 8.4 | Q 4 | Page 79

Find the unit vectors perpendicular to each of the vectors `vec"a" + vec"b"` and `vec"a" - vec"b"`, where `vec"a" = hat"i" + hat"j" + hat"k"` and `vec"b" = hat"i" + 2hat"j" + 3hat"k"`

Exercise 8.4 | Q 5 | Page 80

Find the area of the parallelogram whose two adjacent sides are determined by the vectors  `hat"i" + 2hat"j" + 3hat"k"` and `3hat"i" - 2hat"j" + hat"k"`

Exercise 8.4 | Q 6 | Page 80

Find the area of the triangle whose vertices are A(3, – 1, 2), B(1, – 1, – 3) and C(4, – 3, 1)

Exercise 8.4 | Q 7 | Page 80

If `vec"a", vec"b", vec"c"` are position vectors of the vertices A, B, C of a triangle ABC, show that the area of the triangle ABC is `1/2 |vec"a" xx vec"b" + vec"b" xx vec"c" + vec"c" xx vec"a"|`. Also deduce the condition for collinearity of the points A, B, and C

Exercise 8.4 | Q 8 | Page 80

For any vector `vec"a"` prove that `|vec"a" xx hat"i"|^2 + |vec"a" xx hat"j"|^2 + |vec"a" xx hat"k"|^2 = 2|vec"a"|^2`

Exercise 8.4 | Q 9 | Page 80

Let `vec"a", vec"b", vec"c"` be unit vectors such that `vec"a" * vec"b" = vec"a"*vec"c"` = 0 and the angle between `vec"b"` and `vec"c"` is `pi/3`. Prove that `vec"a" = +-  2/sqrt(3) (vec"b" xx vec"c")`

Exercise 8.4 | Q 10 | Page 80

Find the angle between the vectors `2hat"i" + hat"j" - hat"k"` and `hat"i" + 2hat"j" + hat"k"` using vector product

Exercise 8.5 [Pages 80 - 82]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 8 Vector AlgebraExercise 8.5 [Pages 80 - 82]

Exercise 8.5 | Q 1 | Page 80

Choose the correct alternative:
The value of `vec"AB" + vec"BC" + vec"DA" + vec"CD"` is

  • `vec"AD"`

  • `vec"CA"`

  • `vec0`

  • `- vec"AD"`

Exercise 8.5 | Q 2 | Page 80

Choose the correct alternative:
If `vec"a" + 2vec"b"` and `3vec"a" + "m"vec"b"` are parallel, then the value of m is

  • 3

  • `1/3`

  • 6

  • `1/6`

Exercise 8.5 | Q 3 | Page 80

Choose the correct alternative:
The unit vector parallel to the resultant of the vectors `hat"i" + hat"j" - hat"k"` and `hat"i" - 2hat"j" + hat"k"` is

  • `(hat"i" - hat"j" + hat"k")/sqrt(5)`

  • `(2hat"i" + hat"j")/sqrt(5)`

  • `(2hat"i" - hat"j" + hat"k")/sqrt(5)`

  • `(2hat"i" - hat"j")/sqrt(5)`

Exercise 8.5 | Q 4 | Page 80

Choose the correct alternative:
A vector `vec"OP"` makes 60° and 45° with the positive direction of the x and y axes respectively. Then the angle between `vec"OP"` and the z-axis is

  • 45°

  • 60°

  • 90°

  • 30°

Exercise 8.5 | Q 5 | Page 80

Choose the correct alternative:
If `vec"BA" = 3hat"i" + 2hat"j" + hat"k"` and the position vector of is `hat"i" + 3hat"j" - hat"k"`, then the position vector A is

  • `4hat"i" + 2hat"" + hat"k"`

  • `4hat"i" + 5hat"j"`

  • `4hat"i"`

  • `- 4hat"i"`

Exercise 8.5 | Q 6 | Page 80

Choose the correct alternative:
A vector makes equal angle with the positive direction of the coordinate axes. Then each angle is equal to

  • `cos^-1 (1/3)`

  • `cos^-1 (2/3)`

  • `cos^-1 (1/sqrt3)`

  • `cos^-1 (2/sqrt3)`

Exercise 8.5 | Q 7 | Page 81

Choose the correct alternative:
The vectors `vec"a" - vec"b", vec"b" - vec"c", vec"c" - vec"a"` are

  • parallel to each other

  • unit vectors

  • mutually perpendicular vectors

  • coplanar vectors

Exercise 8.5 | Q 8 | Page 81

Choose the correct alternative:
If ABCD is a parallelogram, then `vec"AB" + vec"AD" + vec"CB" + vec"CD"` is equal to

  • `2(vec"AB" + vec"AD")`

  • `4vec"AC"`

  • `vec"BD"`

  • `vec0`

Exercise 8.5 | Q 9 | Page 81

Choose the correct alternative:
One of the diagonals of parallelogram ABCD with `vec"a"` and `vec"b"` as adjacent sides is `vec"a" + vec"b"`. The other diagonal `vec"BD"` is

  • `vec"a" - vec"b"`

  • `vec"b" - vec"a"`

  • `vec"a" + vec"b"`

  • `(vec"a" + vec"b")/2`

Exercise 8.5 | Q 10 | Page 81

Choose the correct alternative:
If `vec"a", vec"b"` are the position vectors A and B, then which one of the following points whose position vector lies on AB, is

  • `vec"a" + vec"b"`

  • `(2vec"a" - vec"b")/2`

  • `(2vec"a" + vec"b")/3`

  • `(vec"a" - vec"b")/3`

Exercise 8.5 | Q 11 | Page 81

Choose the correct alternative:
If `vec"a", vec"b", vec"c"` are the position vectors of three collinear points, then which of the following is true?

  • `vec"a" = vec"b" + vec"c"`

  • `2vec"a" = vec"b" + vec"c"`

  • `vec"b" = vec"c" + vec"a"`

  • `4vec"a" + vec"b" + vec"c"` = 0

Exercise 8.5 | Q 12 | Page 81

Choose the correct alternative:
If `vec"r" = (9vec"a" + 7vec"b")/16`, then the point P whose position vector `vec"r"` divides the line joining the points with position vectors `vec"a"` and `vec"b"` in the ratio

  • 7 : 9 internally

  • 9 : 7 internally

  • 9 : 7 externally

  • 7 : 9 externally

Exercise 8.5 | Q 13 | Page 81

Choose the correct alternative:
If `lambdahat"i" + 2lambdahat"j" + 2lambdahat"k"` is a unit vector, then the value of `lambda` is

  • `1/3`

  • `1/4`

  • `1/9`

  • `1/2`

Exercise 8.5 | Q 14 | Page 81

Choose the correct alternative:
Two vertices of a triangle have position vectors `3hat"i" + 4hat"j" - 4hat"k"` and `2hat"i" + 3hat"j" + 4hat"k"`. If the position vector of the centroid is `hat"i" + 2hat"j" + 3hat"k"`, then the position vector of the third vertex is

  • `- 2hat"i" - hat"j" + 9hat"k"`

  • `- 2hat"i" - hat"j" - 6hat"k"`

  • `2hat"i" - hat"j" + 6hat"k"`

  • `- 2hat"i" + hat"j" - 6hat"k"`

Exercise 8.5 | Q 15 | Page 81

Choose the correct alternative:
If `|vec"a" + vec"b"| = 60, |vec"a" - vec"b"| = 40` and `|vec"b"| = 46`, then `|vec"a"|` is

  • 42

  • 12

  • 22

  • 32

Exercise 8.5 | Q 16 | Page 81

Choose the correct alternative:
If `vec"a"` and `vec"b"` having same magnitude and angle between them is 60° and their scalar product `1/2` is then `|vec"a"|` is

  • 2

  • 3

  • 7

  • 1

Exercise 8.5 | Q 17 | Page 81

Choose the correct alternative:
The value of θ ∈ `(0, pi/2)` for which the vectors `"a" = (sin theta)hat"i" = (cos theta)hat"j"` and `vec"b" = hat"i" - sqrt(3)hat"j" + 2hat"k"` are perpendicular, equaal to

  • `pi/3`

  • `pi/6`

  • `pi/4`

  • `pi/2`

Exercise 8.5 | Q 18 | Page 82

Choose the correct alternative:
If `|vec"a"| = 13, |vec"b"| = 5` and `vec"a" * vec"b"` = 60° then `|vec"a" xx vec"b"|` is  

  • 15

  • 35

  • 45

  • 25

Exercise 8.5 | Q 19 | Page 82

Choose the correct alternative:
Vectors `vec"a"` and `vec"b"` are inclined at an angle θ = 120°. If `vec"a"| = 1, |vec"b"| = 2`, then `[(vec"a" + 3vec"b") xx (3vec"a" - vec"b")]^2` is equal to

  • 225

  • 275

  • 325

  • 300

Exercise 8.5 | Q 20 | Page 82

Choose the correct alternative:
If `vec"a"` and `vec"b"` are two vectors of magnitude 2 and inclined at an angle 60°, then the angle between `vec"a"` and `vec"a" + vec"b"` is

  • 30°

  • 60°

  • 45°

  • 90°

Exercise 8.5 | Q 21 | Page 82

Choose the correct alternative:
If the projection of `5hat"i" -  hat"j" - 3hat"k"` on the vector `hat"i" + 3hat"j" + lambdahat"k"` is same as the projection of `hat"i" + 3hat"j" + lambdahat"k"` on `5hat"i" -  hat"j" - 3hat"k"`, then λ is equal to

  • ± 4

  • ± 3

  • ± 5

  • ± 1

Exercise 8.5 | Q 22 | Page 82

Choose the correct alternative:
If (1, 2, 4) and (2, – 3λ – 3) are the initial and terminal points of the vector `hat"i" + 5hat"j" - 7hat"k"` then the value of λ is equal to

  • `7/3`

  • `-  7/3`

  • ` - 5/3`

  • `5/3`

Exercise 8.5 | Q 23 | Page 82

Choose the correct alternative:
If the points whose position vectors `10hat"i" + 3hat"j", 12hat"i" - 5hat"j"` and `"a"hat"i" + 11hat"j"` are collinear then a is equal to

  • 6

  • 3

  • 5

  • 8

Exercise 8.5 | Q 24 | Page 82

Choose the correct alternative:
If `vec"a" = hat"i" + hat"j" + hat"k", vec"b" = 2hat"i" + xhat"j" + hat"k", vec"c" = hat"i" - hat"j" + 4hat"k"` and `vec"a" * (vec"b" xx vec"c")` = 70, then x is equal to

  • 5

  • 7

  • 26

  • 10

Exercise 8.5 | Q 25 | Page 82

Choose the correct alternative:
If `vec"a" = hat"i" + 2hat"j" + 2hat"k", |vec"b"|` = 5 and the angle between `vec"a"` and `vec"b"` is `pi/6`, then the area of the triangle formed by these two vectors as two sides, is

  • `7/4`

  • `15/4`

  • `3/4`

  • `17/4`

Chapter 8: Vector Algebra

Exercise 8.1Exercise 8.2Exercise 8.3Exercise 8.4Exercise 8.5
Class 11th Mathematics Volume 1 and 2 Answers Guide - Shaalaa.com

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 8 - Vector Algebra

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 8 (Vector Algebra) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Tamil Nadu Board of Secondary Education Class 11th Mathematics Volume 1 and 2 Answers Guide solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Tamil Nadu Board Samacheer Kalvi textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 8 Vector Algebra are Introduction to Vector Algebra, Scalars and Vectors, Representation of a Vector and Types of Vectors, Algebra of Vectors, Position Vectors, Resolution of Vectors, Direction Cosines and Direction Ratios of a Line, Product of Vectors.

Using Tamil Nadu Board Samacheer Kalvi Class 11th solutions Vector Algebra exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Tamil Nadu Board Samacheer Kalvi Solutions are important questions that can be asked in the final exam. Maximum students of Tamil Nadu Board of Secondary Education Class 11th prefer Tamil Nadu Board Samacheer Kalvi Textbook Solutions to score more in exam.

Get the free view of chapter 8 Vector Algebra Class 11th extra questions for Class 11th Mathematics Volume 1 and 2 Answers Guide and can use Shaalaa.com to keep it handy for your exam preparation

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