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Question

a0,a×b=a×cb=c

A
True
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B
False
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Solution

The correct option is B False
It is given that a0 and a×b=a×c
a×b = a×c can be written as a×(bc)=0
Now cross product of two vectors is zero when
1) Either of the two or both vectors are zero
Or
2) They are parallel to each other.
It is given that a0
So
either a is parallel to bc
or bc = 0 i.e., b=c

So a×b=a×c will imply following
Either b=c
or a is parallel to bc

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