JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \((\alpha, \beta, \gamma)\) be mirror image of the point \((2,3,5)\) in the line \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\). Then \(2 \alpha+3 \beta+4 \gamma\) is equal to
- A \(32\)
- B \(33\)
- C \(31\)
- D \(34\)
Answer & Solution
Correct Answer
(B) \(33\)
Step-by-step Solution
Detailed explanation
\(\because \overrightarrow{\mathrm{PR}} \perp(2,3,4) \) \(\therefore \overrightarrow{\mathrm{PR}} \cdot(2,3,4)=0 \) \((\alpha-2, \beta-3, \gamma-5) \cdot(2,3,4)=0 \) \(\Rightarrow 2 \alpha+3 \beta+4 \gamma=4+9+20=33\)
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