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Question

If v and w are two mutually perpendicular unit vectors and u=av+bw, where a and b are non-zero real number, then the angle between u and w is

A
cos1(ba2+b2)
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B
cos1(aa2+b2)
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C
cos1(b)
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D
cos1(a)
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Solution

The correct option is A cos1(ba2+b2)
We have, u=av+bw
u.w=av.w+bw.w=a(0)+bw2 (v,w are )
=b (w is unit vecotr )
|u||w|cosθ=ba2+b2cosθ=b(|w|=1)
cosθ=ba2+b2θ=cos1(ba2+b2)

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