Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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
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"|`
Find `vec"a"*vec"b"` when `vec"a" = hat"i" - 2hat"j" + hat"k"` and `vec"b" = 3hat"i" - 4hat"j" - 2hat"k"`
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 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"`
Find the angle between the vectors
`2hat"i" + 3hat"j" - 6hat"k"` and `6hat"i" - 3hat"j" + 2hat"k"`
Find the projection of the vector `hat"i" + 3hat"j" + 7hat"k"` on the vector `2hat"i" + 6hat"j" + 3hat"k"`
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 area of the triangle whose vertices are A(3, –1, 2), B(1, –1, –3) and C(4, –3, 1)
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:
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 `|vec"a"| = 13, |vec"b"| = 5` and `vec"a" * vec"b"` = 60° then `|vec"a" xx 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 `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
