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Question

If u, v, w are non-coplanar vectors and p,q are real numbers, then the equality [3upvpw][pvqwu][2wqvqu]=0 holds for

A
exactly two values of (p,q)
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B
more than two but not all values of (p,q)
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C
all values of (p,q)
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D
exactly one value of (p,q)
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Solution

The correct option is D exactly one value of (p,q)
Given:
[3upvpw][pvqwu][2wqvqu]=0
3p2[uvw]pq[vwu]2q2[wvu]=0
(3p2pq+2q2)[uvw]=0
As [uvw]0
(3p2pq+2q2)=0
2p2+p2pq+q24+7q24=0
2p2+(pq2)2+7q24=0
p=0, q=0, p=q2
only possible when p=q=0

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