# 3D vectors and planes

• December 17th 2007, 10:50 AM
ineedhelp
3D vectors and planes
Find the equation for the plane through P(1,e,pi) perpendicular to the vector from the origin to P.
• December 17th 2007, 12:08 PM
Soroban
Hello, ineedhelp!

Quote:

Find the equation for the plane through $P(1,\,e,\,\pi)$
perpendicular to the vector from the origin to $P.$

We are given a point on the plane: $P(1,\,e,\,\pi)$
. . and the normal vector to the plane: . $\vec{n} \:=\:\langle1,\,e,\,\pi\rangle$

The equation is: . $1(x-1) + e(y-e) + \pi(z-\pi) \:=\:0\quad\Rightarrow\quad\boxed{\;x + ey - \pi z \:=\:e^2 + \pi^2 + 1\;}$

• December 17th 2007, 12:16 PM
ineedhelp
I'm not sure why I didn't see that right away.