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Question


If a,b, c and d are unit vectors such that (a×b).(c×d)=1 and a.c=12, then

A
a,b, c are non-coplanar
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B
b, c,d are non-coplanar
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C
a,b, c and d are coplanar vectors
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D
a,d are parallel and b, c are parallel
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Solution

The correct option is C a,b, c and d are coplanar vectors
(¯aׯb).(¯cׯd)
=|¯aׯb||¯cׯd|cosθ
=1
Hence
For this to be true,
(¯aׯb)||(¯cׯd) and |¯aׯb|=|¯cׯd|=1
Hence
¯a,¯b,¯c,¯d are coplanar vectors.

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