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Question

If u,v,w are non-coplanar vectors and p,q are real numbers then the equality [3u pv pw][pv w qu]+[2w qv qu]=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 B more than two but not all values of (p,q)
Given :
[3u pv pw][pv w qu]+[2w qv qu]=03p2[u v w]pq[u v w]2q2[u v w]=0[u v w](3p2pq2q2)=03p2pq2q2=0;([u v w]0)(pq)(3p+2q)=0
p=q or p=23q
so, there are more than two values of (p,q) but not all values of (p,q)

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