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Question

Let a=^i2^j+^k and b=^i^j+^k be two vectors. If c is a vector such that b×c=b×a and ca=0, then cb is equal to :

A
12
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B
32
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C
12
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D
1
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Solution

The correct option is C 12
a=^i2^j+^k
b=^i^j+^k
b×c=b×a
a×(b×c)=a×(b×a)
(ac)b(ab)c=(aa)b(ab)a
(ab)c=(aa)b(ab)a
4c=6(^i^j+^k)4(^i2^j+^k)
c=12(^i+^j+^k)
bc=12

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