Hey everyone, this is my first post here, so here goes:
I'm stuck on a question right now for an assignment, the question is:
Show that the line:
x = 2 + t, y = -3 + 2t, z = 1 + 4t
is parallel to the plane
2y - z = 1.
What is the distance between the line and the plane?
I determined that the vector of the line is (1, 2, 4), from the given equation. With a provided point of (2, -3, 1) from the equation.
I determined the normal of the plane to be (0, 2, -1) from the provided plane equation.
To be parallel, the dot product of the normal and the vector of the line must be zero. This proves the line and the normal of the plane are orthogonal. So: (0, 2, -1) dot (1, 2, 4) must = 0.
4 - 4 = 0, so yes, the line and the plane are parallel.
Here's where I am having difficulty: How do I determine the distance between the line and the plane? Do I substitute the point (2, -3, 1) into the plane equation?
I'm lost here, thanks for your help!