JEE Mains · Maths · STD 12 - 11. three dimension geometry
Consider a line \(\mathrm{L}\) passing through the points \(\mathrm{P}(1,2,1)\) and \(\mathrm{Q}(2,1,-1)\). If the mirror image of the point \(\mathrm{A}(2,2,2)\) in the line \(\mathrm{L}\) is \((\alpha, \beta, \gamma)\), then \(\alpha+\beta+6 \gamma\) is equal to ...........
- A \(6\)
- B \(7\)
- C \(3\)
- D \(12\)
Answer & Solution
Correct Answer
(A) \(6\)
Step-by-step Solution
Detailed explanation
\(DR'\)s of Line \(L \equiv-1: 1: 2\) \(DR'\) s of \(A B \equiv \alpha-2: \beta-2: \gamma-2\) \(\mathrm{AB} \perp_{\mathrm{ar}} \mathrm{L} \Rightarrow 2-\alpha+\beta-2+2 \gamma-4=0\) \(2 \gamma+\beta-\alpha=4\) Let \(C\) is mid-point of \(A B\)…
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