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The plane which bisects the line joining the points \left ( 4,-2,3 \right ) and \left ( 2,4,-1 \right ) at right angles also passes through the point :
Option: 1 (4,0,1)
Option: 2 (0,-1,1)
Option: 3 (4,0,-1)
Option: 4 (0,1,-1)

Answers (1)

best_answer

\begin{aligned} & \mathrm{PA}=\mathrm{PB} \\ \Rightarrow & \mathrm{PA}^{2}=\mathrm{PB}^{2} \\ \Rightarrow &(\alpha-4)^{2}+(\beta+2)^{2}+(\gamma+3)^{2} \\ &=(\alpha-2)^{2}+(\beta-4)^{2}+(\gamma+1)^{2} \\ \Rightarrow &-4 \alpha+12 \beta-8 \gamma=-8 \\ \Rightarrow & 2 \mathrm{x}-6 \mathrm{y}+4 \mathrm{z}=4 \end{aligned}

(4,0,-1) lies in this plane

Posted by

himanshu.meshram

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