JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \((\alpha, \beta, \gamma)\) be the image of the point \(P (2,3,5)\) in the plane \(2 x + y -3 z =6\). Then \(\alpha+\beta+\gamma\) is equal to
- A \(10\)
- B \(5\)
- C \(12\)
- D \(9\)
Answer & Solution
Correct Answer
(A) \(10\)
Step-by-step Solution
Detailed explanation
\(\frac{\alpha-2}{2}=\frac{\beta-3}{1}=\frac{\gamma-5}{-3}=-2\left(\frac{2 \times 2+3-3 \times 5-6}{2^2+1^2+1-3^2}\right)=2\) \(\frac{\alpha-2}{2}=2\) \(\alpha=6\) \(\beta-3=2\) \(\beta=5\) \(\gamma-5=-6\) \(\gamma=-1\) \(\alpha+\beta+\gamma=10\)
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