JEE Main 2022 · 29 Jun · Shift 2 · Mathematics Q14

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MathematicsSingle correct+4 / -1Question 14 of 90

Let Q be the mirror image of the point $P(1,2,1)$ with respect to the plane $x+2y+2z=16$ . Let T be a plane passing through the point Q and contains the line $\vec r=-\hat k+\lambda\left(\hat i+\hat j+2\hat k\right)$ , $\lambda\in\mathbb R$ . Then, which of the following points lies on T?

(2, 1, 0)

(1, 2, 1)

(1, 2, 2)

(1, 3, 2)

Answer and worked solution

Official answer: B

Image. $1+4+2-16=-9$ , so $Q=P+2(1,2,2)=(3,6,5)$ .

Plane T through $(0,0,-1)$ with directions $(1,1,2)$ and $(3,6,6)$ : normal $(-6,0,3)$ , i.e. $2x-z=1$ . The point $(1,2,1)$ satisfies it.

(B)

Topics:Equation of a plane Angles and distances

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JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 14