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 vecr=- hatk+λ( hati+ hatj+2 hatk), λ ∈ R. Then, which of the following points lies on T?

Question

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 vecr=- hatk+λ( hati+ hatj+2 hatk), λ ∈ R. Then, which of the following points lies on T? (A) (2,1,0) (B) (1,2,1) (C) (1,2,2) (D) (1,3,2)

Tardigrade Admin · Accepted Answer

Image of P (1,2,1) in x +2 y +2 z -16=0 is given by Q (4,8,7) Eq. of plane T =| x y z +1 4 8 6 1 1 2|=0 ⇒ 2 x - z =1 so B (1,2,1) lies on it.

Q. 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 $r = - \hat{k} + λ (\hat{i} + \hat{j} + 2 \hat{k}), λ \in R$ . Then, which of the following points lies on $T$ ?

$(2, 1, 0)$

$(1, 2, 1)$

$(1, 2, 2)$

$(1, 3, 2)$

Image of $P (1, 2, 1)$ in $x + 2 y + 2 z - 16 = 0$
is given by $Q (4, 8, 7)$
Eq. of plane $T = ∣ ∣ x 41 y 81 z + 1 62 ∣ ∣ = 0$
$\Rightarrow 2 x - z = 1$ so $B (1, 2, 1)$ lies on it.

Q. 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 r=−k^+λ(i^+j^​+2k^),λ∈R. Then, which of the following points lies on T?

(2,1,0)

(1,2,1)

(1,2,2)

(1,3,2)