Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

We have, foot of the perpendicular drawn from the point (0,0, 0) to the plane is (4, -2, -5).
$\therefore$Direction ratios of normal to the required plane is
$\left(0-\mathrm{4,0}+\mathrm{2,0}+\mathrm{5)}i.e(-\mathrm{4,2},5\right)$
$\therefore$Required equation of plane passing through (4, -2, 5) is
$a\left(x-x_1\right)+b\left(y-y_1\right)+c\left(z-z_1\right)=0$
$\Rightarrow \left(-4\right)\left(x-4\right)+\left(-2\right)\left(y+2\right)+\left(5\right)\left(z+5\right)=0$
$\Rightarrow -4x+2y+5z+16+4+25=0$
$\Rightarrow 4x-2y-5z=45$