JEE Mains · Maths · STD 12 - 11. three dimension geometry
If the image of the point \(P\left( {1, - 2,3} \right)\) in the plane , \(2x + 3y - 4z + 22 = 0\) measured parallel to line , \(\frac{x}{1} = \frac{y}{4} = \frac{z}{5}\) is \(Q\) , then \(PQ \) is equal to :
- A \(6\sqrt 5 \)
- B \(3\sqrt 5 \)
- C \(2\sqrt {42} \)
- D \(\sqrt {42} \)
Answer & Solution
Correct Answer
(C) \(2\sqrt {42} \)
Step-by-step Solution
Detailed explanation
\(\text { Equation of line } \mathrm{PQ} \text { is } \frac{x-1}{1}=\frac{y+2}{4}=\frac{z-3}{5}\) \(\text { Let } \mathrm{F} \text { be }(\lambda+1,4 \lambda-2,5 \lambda+3)\) Since Flies on the plane \(\therefore 2(\lambda+1)+3(4 \lambda-2)-4(5 \lambda+3)+22=0\)…
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