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

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- Dec 17th 2007, 10:50 AMineedhelp3D vectors and planes
Find the equation for the plane through P(1,e,pi) perpendicular to the vector from the origin to P.

- Dec 17th 2007, 12:08 PMSoroban
Hello, ineedhelp!

Exactly*where*is your difficulty?

Quote:

Find the equation for the plane through $\displaystyle P(1,\,e,\,\pi)$

perpendicular to the vector from the origin to $\displaystyle P.$

We are given a point on the plane: $\displaystyle P(1,\,e,\,\pi)$

. . and the normal vector to the plane: .$\displaystyle \vec{n} \:=\:\langle1,\,e,\,\pi\rangle$

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

- Dec 17th 2007, 12:16 PMineedhelp
I'm not sure why I didn't see that right away.