Tamil Nadu Board of Secondary EducationHSC Science Class 11th

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

## Chapter 8: Vector Algebra

Exercise 8.1Exercise 8.2Exercise 8.3Exercise 8.4Exercise 8.5
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

## 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.

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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.

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