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Question

The vectors a and b are not perpendicular and c and d are two vectors satisfying : b×c=b×d and a×d=0. Then the vector d is equal to

A
b+(b.ca.b)c
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B
c(aca.b)b
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C
b(b.ca.b)c
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D
c+(aca.b)b
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Solution

The correct option is B c(aca.b)b
ab0 (given)
ad=0
Now, b×c=b×da×(b×c)=a×(b×d)
(ac)b(ab)c=(ad)b(ab)d
(ab)d=(ac)b+(ab)c
d=(ac)(ab)+c.

1257533_1329196_ans_b64522da1db04216aaed2a42b87f856c.PNG

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