मराठी
तामिळनाडू बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान इयत्ता ११

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

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • `cos^-1 (1/3)`

  • `cos^-1 (2/3)`

  • `cos^-1 (1/sqrt3)`

  • `cos^-1 (2/sqrt3)`

MCQ
Advertisements

उत्तर

`cos^-1 (1/sqrt3)`

shaalaa.com
Product of Vectors
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Vector Algebra - Exercise 8.5 [पृष्ठ ८०]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 8 Vector Algebra
Exercise 8.5 | Q 6 | पृष्ठ ८०

संबंधित प्रश्‍न

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


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"|`


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"|`


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"`


Find the angle between the vectors

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


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


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


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


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


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`


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


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


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


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


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


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


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×