JEE Mains · Maths · STD 12 - 11. three dimension geometry
If \(Q(0, -1, -3)\) is the image of the point \(P\) in the plane \(3x -y+4z = 2\) and \(R\) is the point \((3, -1, -2)\), then the area (in square units) of \(\Delta PQR\) is
- A \(\frac{{\sqrt {91} }}{2}\)
- B \(2\sqrt {13} \)
- C \(\frac{{\sqrt {65} }}{2}\)
- D \(\frac{{\sqrt {91} }}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{{\sqrt {91} }}{2}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{MQ}=\frac{|1-12-2|}{\sqrt{9+1+16}}=\frac{13}{\sqrt{26}}=\sqrt{\frac{13}{2}}\) \(P M=\sqrt{26}\) \(\mathrm{RQ}=\sqrt{9+1}=\sqrt{10}\) \(\mathrm{RM}=\sqrt{10-\frac{13}{2}}=\sqrt{\frac{7}{2}}\)…
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