Plane through a point with given normal

Statement

Write the equation of the plane passing through $P_0(1;1;1)$ and perpendicular to $\vec n=(2;-1;3)$.

Solution

With normal $(a,b,c)=(2;-1;3)$ the plane is $2x-y+3z+d=0$, where $d = -(2\cdot 1 - 1\cdot 1 + 3\cdot 1) = -4.$ Therefore $\boxed{2x-y+3z-4=0}.$

Links

Topics: Analytic geometry in space
Concepts: Equation of the plane · Plane · Normal vector
Skills: Analytic geometry · Using formulae
Exercise types: Geometric problem