Advertisements
Advertisements
Question
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
Options
`pi/3`
`pi/6`
`pi/4`
`pi/2`
Solution
`pi/3`
APPEARS IN
RELATED QUESTIONS
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
`tan theta/2 = |vec"a" - vec"b"|/|vec"a" + vec"b"|`
Find `vec"a"*vec"b"` when `vec"a" = hat"i" - 2hat"j" + hat"k"` and `vec"b" = 3hat"i" - 4hat"j" - 2hat"k"`
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"`
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"`
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
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`
Find the angle between the vectors `2hat"i" + hat"j" - hat"k"` and `hat"i" + 2hat"j" + hat"k"` using vector product
Choose the correct alternative:
The vectors `vec"a" - vec"b", vec"b" - vec"c", vec"c" - vec"a"` are
Choose the correct alternative:
If `lambdahat"i" + 2lambdahat"j" + 2lambdahat"k"` is a unit vector, then the value of `lambda` is
Choose the correct alternative:
If `|vec"a" + vec"b"| = 60, |vec"a" - vec"b"| = 40` and `|vec"b"| = 46`, then `|vec"a"|` is
Choose the correct alternative:
If `|vec"a"| = 13, |vec"b"| = 5` and `vec"a" * vec"b"` = 60° then `|vec"a" xx vec"b"|` is
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 (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" + 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