Question:
The plane which bisects the line joining the points $(4,-2,3)$ and $(2,4,-1)$ at right angles also passes through the point:
Correct Option: 1
Solution:
$\mathrm{PA}=\mathrm{PB}$
$\Rightarrow \quad \mathrm{PA}^{2}=\mathrm{PB}^{2}$
$\Rightarrow \quad(\alpha-4)^{2}+(\beta+2)^{2}+(\gamma-3)^{2}$
$=(\alpha-2)^{2}+(\beta-4)^{2}+(\gamma+1)^{2}$
$\Rightarrow \quad-4 \alpha+12 \beta-8 \gamma=-8$
$\Rightarrow \quad 2 x-6 y+4 z=4$
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