JEE Mains · Maths · STD 12 - 11. three dimension geometry
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 \(\vec{r}=-\hat{k}+\lambda(\hat{i}+\hat{j}+2 \hat{k}), \lambda \in R\). Then, which of the following points lies on \(T\) ?
- A \((2,1,0)\)
- B \((1,2,1)\)
- C \((1,2,2)\)
- D \((1,3,2)\)
Answer & Solution
Correct Answer
(B) \((1,2,1)\)
Step-by-step Solution
Detailed explanation
Image of \(P(1,2,1)\) in \(x+2 y+2 z-16=0\) is given by \(Q (4,8,7)\) Eq. of plane \(T =\left|\begin{array}{ccc} x & y & z +1 \\ 4 & 8 & 6 \\ 1 & 1 & 2\end{array}\right|=0\) \(\Rightarrow 2 x - z =1\) so \(B (1,2,1)\) lies on it.
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