I need help finding it. The question is below:
13. A plane has normal vector n = [3, -1, 4] and passes through the point A(1, 2, 5).
a) Determine the scalar equation of the plane.
b) Determine parametric equations of the plane.
For a I got 3x-y+4z-20=0, which is correct. However, for the parametric equation I got, x = 1+3t, y=2-t, and z=5+4t. The book says this is wrong. In fact it has two variables in it, s and t. Where do they get the second variable? How do they do part b?
Also how does one know if a line and a plane intersect? For example, how would you show that ((x+4)/2)=((y+2)/3)=99z-3)/2) intersects with plane 3x-y+2z-3=0.