If be any point on the plane and be a point on the line such that

MATHEMATICS · Subjective · CBSE · Mathematics · Three-Dimensional Geometry · IB Diploma Programme

Problem

If PP be any point on the plane lx+my+nz=plx + my + nz = p and QQ be a point on the line OPOP such that OP⋅OQ=p2OP \cdot OQ = p^2, show that the locus of the point QQ is p(lx+my+nz)=x2+y2+z2p(lx + my + nz) = x^2 + y^2 + z^2.

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