Find the value of so that the points and on the sides and

MATHEMATICS · Single correct · ISC · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

Find the value of

\lambda

so that the points

P, Q, R

and

S

on the sides

OA, OB, OC

and

AB

, respectively, of a regular tetrahedron

OABC

are coplanar. It is given that

\frac{OP}{OA} = \frac{1}{3}, \frac{OQ}{OB} = \frac{1}{2}, \frac{OR}{OC} = \frac{1}{3}

and

\frac{OS}{AB} = \lambda

. (1)

\lambda = \frac{1}{2}

(2)

\lambda = -1

(3)

\lambda = 0

(4) for no value of

\lambda