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

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(1, 3, 2)

(1, 2, 2)

(1, 2, 1)

(2, 1, 0)

answer is B.

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Detailed Solution

Image of P(1, 2, 1) in x + 2y + 2z – 16 = 0
is given by Q(4, 8, 7)
Eq. of plane $T = |\begin{array}{ccc} x & y & z + 1 \\ 4 & 8 & 6 \\ 1 & 1 & 2 \end{array}| = 0$
$\Rightarrow$ 2x - z = 1 so B(1, 2, 1) lies on it.

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