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Find the value of so that the points {P},{Q},{R} and {S} on t

Question

Find the value of $λ$ so that the points $P, Q, R$ and $S$ on the sides $O A, O B, O C$ and $A B,$ respectively, of a regular tetrahedron $O A B C$ are coplanar. It is given that $\frac{O P}{O A} = \frac{1}{3}, \frac{O Q}{O B} = \frac{1}{2}, \frac{O R}{O C} = \frac{1}{3}$ and $\frac{O S}{A B} = λ ˙$ (A) $λ = \frac{1}{2}$ (B) $λ = - 1$ (C) $λ = 0$ (D) for no value of $λ$

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Theodore Discussed

Find the value of

λ

so that the points

P, Q, R

and

S

on the sides

O A, O B, O C

and

A B,

respectively, of a regular tetrahedron

O A B C

are coplanar. It is given that

\frac{O P}{O A} = \frac{1}{3}, \frac{O Q}{O B} = \frac{1}{2}, \frac{O R}{O C} = \frac{1}{3}

and

\frac{O S}{A B} = λ ˙

(A)

λ = \frac{1}{2}

(B)

λ = - 1

(C)

λ = 0

(D) for no value of

λ

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