JEE Mains · Maths · STD 12 - 11. three dimension geometry
A plane \(P\) contains the line of intersection of the plane \(\overrightarrow{ r } \cdot(\hat{i}+\hat{j}+\hat{k})=6\) and \(\overrightarrow{ r } \cdot(2 \hat{i}+3 \hat{j}+4 \hat{ k })=-5\). If \(P\) passes through the point \((0,2,-2)\), then the square of distance of the point \((12,12,18)\) from the plane \(P\) is
- A \(1240\)
- B \(620\)
- C \(310\)
- D \(155\)
Answer & Solution
Correct Answer
(B) \(620\)
Step-by-step Solution
Detailed explanation
Equation of plane \(P\) is \((x+y+z-6)+\lambda(2 x+3 y+4 z+5)=0\) Plane passes through the point \((0,2,-2)\) \(\therefore(2-2-6)+\lambda(6-8+5)=0\) \(-6+\lambda(3)=0\) \(\lambda=2\) Equation of plane \(p\) is \((x+y+z-6)+2(2 x+3 y+4 z+5)=0\) \(5 x+7 y+9 z+4=0\)…
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