Find an equation of the plane

Question

Find an equation of the plane through the point (-5, -1, 1) and perpendicular to the vector (-1, 1, 5). Do this problem in the standard way

Answer 1

If a plane has the equation Ax + By + Cz = D, then the vector normal to it is <A, B, C>

Since you're given the normal vector <-1, 1, 5>, the plane will be of the form

 

-x + y + 5z = D

 

You can then plug in the point given to find the value of D.