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The angle between two vectors given by 6...

The angle between two vectors given by `6hat(i)+6hat(j)-3hat(k)` and `7hat(i)+4hat(j)+4hat(k)` is

A

`cos^(-1)(1/(sqrt(3)))`

B

`cos^(-1)(5/(sqrt(3)))`

C

`sin^(-1)(2/(sqrt(3)))`

D

`sin^(-1)(sqrt(5)/3)`

Text Solution

Verified by Experts

The correct Answer is:
D
`cos theta = (vec(A).vec(B))/(AB)= (42+24-12)/(sqrt(36+36+9) sqrt(49+16+16))= (54)/(81)`
`cos theta = (54)/(81) :. sin theta = (sqrt(5))/3 or theta = "sin"^(-1)(sqrt(5))/3`
`implies cos theta= 1/(sqrt(2)) :. theta= 45^(@)`
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