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  • Let be a point on the plane which passes through the point <img alt="\left ( 4 ,-2,2 \right )." src="h

Let \left ( \lambda ,2,1 \right ) be a point on the plane which passes through the point \left ( 4 ,-2,2 \right ). If the plane is perpendicular to the line joining the points \left ( -2,-21,29\right ) and \left ( -1,-16,23\right ), then \left ( \frac{\lambda }{11} \right )^{2}-\frac{4\lambda }{11}-4 is equal to _______.
Option: 1 4
Option: 2 6
Option: 3 8
Option: 4 10

Answers (1)

best_answer

Let point A be (-2, -21, 29) and point B be (-1, -16, 23)

and let point P be (\lambda,2,1) and point Q be (4, -2, 2)

Point P and Q lies on the plane.

 

\\\vec{AB}\cdot \vec{PQ}=0

\\\Rightarrow(\hat{\mathrm{i}}+5 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}) \cdot((4-\lambda) \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+\hat{\mathrm{k}})=0 \\ \Rightarrow 4-\lambda-20-6=0 \\ \Rightarrow \lambda=-22

\Rightarrow\left(\frac{\lambda}{11}\right)^{2}-\frac{4 \lambda}{11}-4=4+8-4=8

Posted by

himanshu.meshram

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