Question

If L is the line through the point P=(3,2,1) and parallel to the vector v=⟨2,1,−3⟩, what is an equation of the plane that contains L and the point Q=(−2,3,1)?

Answer 1

3x +15y +7z = 46

Explanation:

The cross product of v = <2, 1, -3> and PQ = <-5, 1, 0> is <3, 15, 7>, the normal vector of the plane of interest. That plane contains P and Q, so the constant in the plane's equation will be ...

<3, 15, 7> · <3, 2, 1> = 46

The desired equation is ...

3x +15y +7z = 46