Question:
Let the plane $a x+b y+c z+d=0$ bisect the line joining the points $(4,-3,1)$ and $(2,3,-5)$ at the right angles. If $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}$ are integers, then the minimum value of $\left(a^{2}+b^{2}+c^{2}+d^{2}\right)$ is
Solution:
Plane is $1(x-3)-3(y-0)+3(z+2)=0$
$x-3 y+3 z+3=0$
$\left(a^{2}+b^{2}+c^{2}+d^{2}\right)_{\min }=28$