Mathematics · 3D Geometry

JEE Advanced 2022 — Paper 1 — Question 11

Let $P_{1}$ and $P_{2}$ be two planes given by $P_{1}: 10 x+15 y+12 z-60=0, P_{2}:-2 x+5 y+4 z-20=0$ .

Which of the following straight lines can be an edge of some tetrahedron whose two faces lie on $P_{1}$ and $P_{2}$ ?

Answer: A, B, D

The line should be either coincident on $P_{1}$ or on $P_{2}$ or intersect on $P_{1}$ and $P_{2}$

on different points.

(D) $\frac{x}{1}=\frac{y-4}{-2}=\frac{z}{3}=\lambda$

$\Rightarrow(\lambda,-2 \lambda+4,3 \lambda)$

lie on $\mathrm{P}_{2}$ .

(A) $\frac{x-1}{0}=\frac{y-1}{0}=\frac{z-1}{5}$ intersects $P_{1}$ and $P_{2}$

on different points.

(B) $\frac{x-6}{5}=\frac{y}{2}=\frac{z}{3}$ also intersects $P_{1}$ and $P_{2}$ on different points.

Answer key and solution verified before publishing.

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