JEE Mains · Maths · STD 12 - 11. three dimension geometry
If the image of the point \(P(1, 2, a)\) in the line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{7-z}{2}\) is \(Q(5,b,c)\), then \(a^{2}+b^{2}+c^{2}\) is equal to
- A 293
- B 264
- C 298
- D 283
Answer & Solution
Correct Answer
(C) 298
Step-by-step Solution
Detailed explanation
Point \(M \equiv\left(3, \frac{b}{2}+1, \frac{ c + a }{2}\right)\) satisfies the line \(\frac{3-6}{3}=\frac{\frac{b}{2}+1-7}{2}=\frac{\frac{c+a}{2}-7}{-2}\)\(-1=\frac{b-12}{4}=\frac{c+a-14}{-4}\) \(\Rightarrow b =8 \quad \ldots\) (1) & \(c + a =18 \ldots\) (2) Now…
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