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Question

The three vectors ^i+^j,^j+^k,^k+^i taken two at a time form three planes The three unit vectors drawn perpendicular to these planes form a parallelopiped of volume

A
13
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B
4
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C
334
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D
433
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Solution

The correct option is C 433
The normal vector of the first plane is given by
(i+j)×(j+k)
=ij+k
Hence unit vector will be
=ij+k3=n1
The normal vector of the second plane is given by
(i+j)×(k+i)
=ijk
Hence unit vector will be
=ijk3=n2
The normal vector of the third plane is given by
(j+k)×(k+i)
=i+jk
Hence unit vector will be
=i+jk3=n3
Hence volume of the parallel-pipe will be
13[n1n2n3]

=433

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