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Question

If ¯v and ¯w are two mutually perpendicular unit vectors and ¯u=a¯v+b¯w, where a and b are non zero real numbers, 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 C cos1(ba2+b2)
We have,
[¯¯¯v]=[¯¯¯u]=1¯¯¯u=a¯¯¯v+b¯¯¯¯w|u|=a2+b2u+θbetheanglebetween¯¯¯uand¯¯¯¯w¯¯¯u.¯¯¯¯w=¯¯¯u¯¯¯¯wcosθ(a¯¯¯v+b¯¯¯¯w).¯¯¯¯w=a2+b2cosθb=a2+b2cosθcosθ=ba2+b2θ=cos1(ba2+b2)
So, correct option is A.

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