Let Q be the mirror image of the point P1, 2, 1 with respect to the plane x+2y+2z=16. Let T be a plane passing through the point Q and contains the…

Question

Let Q be the mirror image of the point P1, 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 r→=-k^+λ(i^+j^+2k^), λ∈R. Then, which of the following points lies on T?

MARKS Content Team · Accepted Answer

Correct answer: (B) 1, 2, 1. We know that by image formula, image of P1, 2, 1 in x+2y+2z-16=0 is given by Q4, 8, 7 Now equation of plane will be given by T= x-x_1 y-y_1 z-z_1 a_1 b_1 c_1 a_2 b_2 c_2 =0 ⇒T= x-0 y-0 z+1 4-0 8-0 7+1 1 1 2 =0 ⇒2x-z=1 Now from options, only point B1, 2, 1 lies on it.

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

Solution

Relevant Questions