The line which contains all points which are of the form intersects the plane at and…

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

Problem

The line which contains all points (x,y,z)(x, y, z) which are of the form (x,y,z)=(2,−2,5)+λ(1,−3,2)(x, y, z) = (2, -2, 5) + \lambda (1, -3, 2) intersects the plane 2x−3y+4z=1632x - 3y + 4z = 163 at PP and intersects the YZYZ -plane at QQ . If the distance PQPQ is aba\sqrt{b} , where a,b∈Na, b \in \mathbb{N} and a>3a > 3 , then (a+b)(a + b) is equal to (1) 23 (2) 95 (3) 27 (4) None of these

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