Question

Find parametric equations for the line that is perpendicular to the plane 2x-y+3z=7 and intersects the plane when x=1 and y=1.

Answer 1

when x=1 and y = 1
in the plane:
2-1 + 3z = 7
z = 2
so the line will intersect at (1,1,2)
and the direction of the line will be (2,-1,3), the normal to the plane

line equation:
x = 1 + 2t
y = 1 - t
z = 2 + 3t