JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \(P\) be a plane \(l x+m y+n z=0\) containing the line, \(\frac{1-x}{1}=\frac{y+4}{2}=\frac{z+2}{3} .\) If plane \(P\) divides the line segment \(AB\) joining points \(A (-3,-6,1)\) and \(B (2,4,-3)\) in ratio \(k : 1\) then the value of \(k\) is equal to
- A \(1.5\)
- B \(3\)
- C \(2\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
Point \(C\) is \(\left(\frac{2 k-3}{k+1}, \frac{4 k-6}{k+1}, \frac{-3 k+1}{k+1}\right)\) \(\frac{x-1}{-1}=\frac{y+4}{2}=\frac{z+2}{3}\) Plane \(l x + my + nz =0\) \(l(-1)+m(2)+n(3)=0\) \(-l+2 m+3 n=0\) \(......(1)\) It also satisfy point \((1,-4,-2)\) \(l-4 m-2 n=0\)…
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