JEE Mains · Maths · STD 12 - 11. three dimension geometry
If the mirror image of the point \((2,4,7)\) in the plane \(3 x-y+4 z=2\) is \((a, b, c)\), the \(2 a+b+2 c\) is equal to
- A \(5\)
- B \(4\)
- C \(-6\)
- D \(-4\)
Answer & Solution
Correct Answer
(C) \(-6\)
Step-by-step Solution
Detailed explanation
\(\frac{a-2}{3}=\frac{b-4}{-1}=\frac{c-7}{4}=\frac{-2(6-4+28-2)}{3^{2}+1^{2}+4^{2}}\) \(\Rightarrow a=\frac{-84}{13}+2, b=\frac{28}{13}+4, C=\frac{-112}{13}+7\) \(\Rightarrow 2 a+b+2 c=-6\)
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