I know that the direction vector of r(t) needs to be orthogonal to the plane's normal vector.Find theof the plane passing through the points (3, 2, -1) and (1, -1, 2) that is to the line r(t) = <1, -1, 0> + t<3, 2, -1>
Let P1 = (3, 2, -1) and P2 = (1, -1, 2) I need a third point P3 such that the cross product of vectors P1P2 x P2P3 is our vector normal N such that the dot product N dot <3, 2, -1> = 0
That's correct, right? How would I setup for this problem to find the equation of the plane passing through P1 and P2 and be parallel to r(t)? Just a bit of advice would be great - would rather not have anyone set it up in entirety.