Advertisements
Advertisements
प्रश्न
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"`
Advertisements
उत्तर
Given `|vec"a"| = 10, |vec"b"| = 15` and `vec"a"*vec"b" = 75sqrt(2)`
Let θ be the angle between `vec"a"` and `vec"b"`
cos θ = `(vec"a"*vec"b")/(|vec"a"| * |vec"b"|)`
= `(75sqrt(2))/(10 xx 15)`
= `sqrt(2)/2`
cos θ = `1/sqrt(2)`
cos θ = `(15 xx 5 xx sqrt(2))/(10 xx 15)`
cos θ = `sqrt(2)/(sqrt(2) xx sqrt(2))`
= `1/sqrt(2)`
θ = 45°
= `pi/4`
APPEARS IN
संबंधित प्रश्न
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 `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
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"|`
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
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"`
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"`
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"`
Find the area of the triangle whose vertices are A(3, –1, 2), B(1, –1, –3) and C(4, –3, 1)
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`
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")`
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
Choose the correct alternative:
A vector makes equal angle with the positive direction of the coordinate axes. Then each angle is equal to
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:
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:
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 `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
