Question

Find the equation of a plane which passes through the point $(1,2,3.)$ and which is at the maximum distance from the point $(-1,0,2)$.

Answer 1

For the plane to be at max. distance,

the plane should be perpendicular to line joining the points

$\Rightarrow$ D's of round of plane = $(1+1,2-0,2-3)=(2,2,2)$

passing through $(1,2,3)$

equating of plane $2x+2y+3+d=0$

$2\left(1\right)+2\left(2\right)+3+d=0$

$\Rightarrow d=-9$

$\therefore$ equation of plane $2x+2y+z=9$