JEE Mains · Maths · STD 12 - 11. three dimension geometry
Consider the lines \(\mathrm{L}_1: \mathrm{x}-1=\mathrm{y}-2=\mathrm{z}\) and \(\mathrm{L}_2: \mathrm{x}-2=\mathrm{y}=\mathrm{z}-1\). Let the feet of the perpendiculars from the point \(\mathrm{P}(5,1,-3)\) on the lines \(\mathrm{L}_1\) and \(\mathrm{L}_2\) be \(Q\) and \(R\) respectively. If the area of the triangle PQR is A , then \(4 \mathrm{~A}^2\) is equal to :
- A 139
- B 147
- C 151
- D 143
Answer & Solution
Correct Answer
(B) 147
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{L}_1: \frac{\mathrm{x}-1}{1}=\frac{\mathrm{y}-2}{1}=\frac{\mathrm{z}-0}{2} \\ & \text { Let } \mathrm{Q}(\lambda+1, \lambda+2, \lambda) \\ & \overrightarrow{\mathrm{PQ}}=(\lambda-4, \lambda-1, \lambda+3) \\ & \overrightarrow{\mathrm{PQ}} \cdot…
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