JEE Mains · Maths · STD 12 - 11. three dimension geometry
A line with direction ratios \(2,1,2\) meets the lines \(x=y+2=z\) and \(x+2=2 y=2 z\) respectively at the point \(P\) and \(Q\). if the length of the perpendicular from the point \((1,2,12)\) to the line \(\mathrm{PQ}\) is \(l\), then \(l^2\) is
- A \(63\)
- B \(65\)
- C \(42\)
- D \(56\)
Answer & Solution
Correct Answer
(B) \(65\)
Step-by-step Solution
Detailed explanation
Let \(\mathrm{P}(\mathrm{t}, \mathrm{t}-2, \mathrm{t})\) and \(\mathrm{Q}(2 \mathrm{~s}-2, \mathrm{~s}, \mathrm{~s})\) \(D.R\)'s of \(PQ\) are \(2, 1,2\) \( \frac{2 s-2-t}{2}=\frac{s-t+2}{1}=\frac{s-t}{2} \) \( \Rightarrow t=6 \text { and } s=2 \)…
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