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Question

Two vectors X and Y have equal magnitude. The magnitude of (XY) is n times the magnitude of (X+Y). The angle between X and Y is:

A
cos1(n2+1n21)
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B
cos1(n2+1n21)
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C
cos1(n21n21)
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D
cos1(n21n21)
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Solution

The correct option is C cos1(n21n21)
Given that, X=Y

Also, XY=nX+Y

X2+Y22XYcosθ=nX2+Y2+2×Ycosθ

Squaring both sides,

2X2(1cosθ)=n2 2X2(1+cosθ)

1cosθ=n2+n2cosθ

cosθ=1n21+n2

θ=cos1[n21n21]

Hence, option (B) is correct.

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