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Question

The vectors a and b are not perpendicular and c and d are two vectors satisfyingb×c=b×d and a·d=0. Then, the vector d is equal to?


A

c+a·ca·db

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B

b+b·ca·bc

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C

c-a·ca·bb

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D

b-b·ca·bc

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Solution

The correct option is C

c-a·ca·bb


Explanation for correct option

The vectors a and b are not perpendicular

So, a.b0

Given, a.d=0

b×c=b×da×(b×c)=a×(b×d)(a·c)b(a·b)c=(a·d)b(a·b)d(a·b)d=-(a.c)b+(a.b)cd=c-a.ca·bb

Hence, option (C) is correct


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