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Question

If p & s are not perpendicular to each other and r×p=q×p & r.s=0, then r=

A
p.s
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B
q+(q.sp.s)p
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C
q(q.sp.s)p
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D
q+μp for all scalars μ
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Solution

The correct option is B q(q.sp.s)p
Let r,p,q and s be vectors.
It is given that
r×p=q×p
r×p(q×p)=0
(rq)×p=0
Hence rq is a vector parallel to vector p.
Hence
r=q+μp ...(i)
It is given that r.s=0.
Hence r vector is perpendicular to s vector.
Hence (q+μp).s=0 ...(from i)
q.s+μ(p.s)=0
μ(p.s)=q.s
μ=q.sp.s
Hence r=qq.sp.sp

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