Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Let the origin be $O(0,0,0)$ and the foot of the perpendicular be $P(2,-1,4)$.

The normal vector to the plane is $\overrightarrow{OP}=2\hat{i}-\hat{j}+4\hat{k}$.

The direction ratios of the normal are $2,-1,4$.

The plane passes through the point $P(2,-1,4)$.

The equation of the plane is given by $a(x-x_1)+b(y-y_1)+c(z-z_1)=0$.

Substituting the values, we get:

$2(x-2)-1(y+1)+4(z-4)=0$

$2x-4-y-1+4z-16=0$

$2x-y+4z-21=0$

Answer: $2x-y+4z-21=0$