The correct option is B p(lx+my+nz)=x2+y2+z2
The given equation of the plane is lx+my+nz=p
Let P(α,β,γ) be a point on the plane and Q(x,y,z) be a point on OP such that OP⋅OQ=p2
⇒lα+mβ+nγ=p
The direction ratios of OP are α,β,γ and OQ are x,y,z.
Since O,P,Q are collinear αx=βy=γz=k .....(1)
⇒OP⋅OQ=√α2+β2+γ2⋅√x2+y2+z2=p2
⇒k(x2+y2+z2)=p2
∴lα+mβ+nγ=p⇒k(lx+my+nz)=p
Hence, the locus of Q is p(lx+my+nz)=x2+y2+z2.