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Question

If x×b=c×b and xa, then x is equal to

A
b×(a×c)b.c
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B
(b×c)×ab.a
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C
a×(c×b)a.b
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D
None of these
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Solution

The correct options are
B (b×c)×ab.a
C a×(c×b)a.b
x×b=c×b.... {1}
Pre-multiplying both sides of {1} by a, we get
a×(x×b)=a×(c×b)
Simplifying the above equation, we get
(ab)x(ax)b=a×(c×b)
x is perpendicular to a;ax=0
x=a×(c×b)ab
Also, b×x=b×c.... {2}
Post-multiplying both sides of {2} by a, we get
(b×x)×a=(b×c)×a)
Simplifying the above equation, we get
(ab)x(ax)b=a×(c×b)
x is perpendicular to a;ax=0
x=(b×c)×aba
Hence, option B,C.

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