JEE Mains · Maths · STD 12 - 11. three dimension geometry
Consider the lines \(L _1\) and \(L _2\) given by \(L_1: \frac{ x -1}{2}=\frac{ y -3}{1}=\frac{ z -2}{2}\) \(L _2: \frac{ x -2}{1}=\frac{ y -2}{2}=\frac{ z -3}{3}\) A line \(L _3\) having direction ratios \(1,-1,-2\), intersects \(L _1\) and \(L _2\) at the points \(P\) and \(Q\) respectively. Then the length of line segment \(PQ\) is
- A \(2 \sqrt{6}\)
- B \(3 \sqrt{2}\)
- C \(4 \sqrt{3}\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(2 \sqrt{6}\)
Step-by-step Solution
Detailed explanation
Let \(P=(2 \lambda+1, \lambda+3,2 \lambda+2)\) Let \(Q=(\mu+2,2 \mu+2,3 \mu+3)\) \(\Rightarrow \frac{2 \lambda-\mu-1}{1}=\frac{\lambda-2 \mu+1}{-1}=\frac{2 \lambda-3 \mu-1}{-2}\) \(\Rightarrow \lambda=\mu=3 \Rightarrow P(7,6,8) \text { and } Q (5,8,12)\) \(PQ =2 \sqrt{6}\)
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