JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let the vertices \(Q\) and \(R\) of the triangle \(P Q R\) lie on the line \(\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}, Q R=5\) and the coordinates of the point \(P\) be \((0,2,3)\). If the area of the triangle \(P Q R\) is \(\frac{m}{n}\) then :
- A \(\mathrm{m}-5 \sqrt{21} \mathrm{n}=0\)
- B \(2 \mathrm{~m}-5 \sqrt{21} \mathrm{n}=0\)
- C \(5 \mathrm{~m}-2 \sqrt{21} \mathrm{n}=0\)
- D \(5 m-21 \sqrt{2} n=0\)
Answer & Solution
Correct Answer
(B) \(2 \mathrm{~m}-5 \sqrt{21} \mathrm{n}=0\)
Step-by-step Solution
Detailed explanation
\(\mathrm{M}(5 \lambda-3,2 \lambda+1,3 \lambda-4)\) Drs of PM \(\Rightarrow 5 \lambda-3,2 \lambda-1,3 \lambda-7\) Drs of line \(L \Rightarrow 5,2,3\) \(\mathrm{PM} \perp \mathrm{L}\) \(\Rightarrow(5 \lambda-3) 5+(2 \lambda-1) 2+(3 \lambda-7) 3=0\) \(\Rightarrow \lambda=1\)…
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