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Question

Let p,q,r be three unit vectors such that p×q=r. If a is any vector such that [a q r]=1,[a r p]=2 and [a p q]=3 then a is

A
p+3q+r
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B
3p+2q+r
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C
p2q3r
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D
p+2q+3r
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Solution

The correct option is D p+2q+3r
(p×q).r=|r|2[p q r]=1
Let a=xp+yq+zr
Take dot product with p×q,q×r and r×p
[a p q]=1=x
Similarly y=2, z=3
a=p+2q+3r

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