Here is my current problem:
Find the equation of the plane that passes through the point (-2, 3, 4) and is perpendicular to the line passing through the points (4, -2, 5) and (0, 2, 4).
Well, I need a vector, which I obtained from the two given points. I get: (-4, 4, -1).
Now, from my understanding, the point on the plane is perpendicular to this point, so I can form the general equation with them:
Equation of plane:
(-4, 4, -1).(x + 2, y - 3, z - 4) = 0
When simplifed to its general form, I get:
-4x + 4y - z = 16
I think that I'm doing it correctly, however, I also feel as though I should be using the cross product. Can anyone point me in the right direction?