Prove that the line x = 1 + 2t, y = -1 + 3t, z = 2 + 4t is parallel to the plane x - 2y + z = 6.
What is the distance between the line and the plane?
not that the vector in the direction of the line is <2,3,4>. we want this to be perpendicular to the normal to the plane, which is <1,-2,1>. as you can see, that does not happen
if you want to find the distance between a plane and a line parallel to it, use the formula:
this gives the distance between a point and the plane , just make sure is a point on the line