Question

If the foot of the perpendicular from the origin to a plane is $(1,2,-3)$, then the equation of the plane is _____

• A. $x+2y-3z=0$
• B. $\frac{x}{1}+\frac{y}{2}+\frac{z}{3}=1$
• C. $x+2y-3z=-6$
• D. $x+2y-3z=14$

Answer 1

The correct option is D $x+2y-3z=14$

given that the point lies on that plane

let the equation of the plane be $ax+by+cz=k$

substituting the point we get

$a+2b-3c=k$

now the dr's of the line joining the origin to the point is $(1,2,-3)$

as it becomes normal to the plane therefor $a=1,b=2,c=-3$

therefore $k=14$

therefore the equation is $x+2y-3z=14$