Im having trouble understanding this Vector plane statement.

"You can find every point in a plane using two non-parallel vectors given a starting position vector"

Why does this work?

It's how a plane is defined; as the span of two non-parallel vectors acting through a starting point.

Intuitively, consider the basic case of the origin on a 2D plane and the vector $\mathbf{i}$ pointing one unit to the right of the origin. You can only travel along this vector by taking scalar multiples of it. You can go as far as you want, or even go in the opposite direction. The point is, the locus of points that you can obtain using a scalar multiple of this vector is just a straight horizontal line through the origin.

If you now introduce a non-parallel vector, say $\mathbf{j}$ pointing one unit upwards from the origin, then you can also travel up/down now as well. So, not only can you travel horizontally as much as you want, but you can also travel vertically as much as you want.

The locus of points with two non-parallel vectors is precisely the 2D plane itself.

Thanks, Makes sense now. Also, I know this wasn't part of the question but when finding the angle between a line and a plane why do you find the angle between the line and the normal to a plane? Shouldn't you use the direction vector which is parallel to the plane? It seems counter-intuitive to use the direction vector which is perpendicular to the plane.

Thanks, Makes sense now. Also, I know this wasn't part of the question but when finding the angle between a line and a plane why do you find the angle between the line and the normal to a plane? Shouldn't you use the direction vector which is parallel to the plane? It seems counter-intuitive to use the direction vector which is perpendicular to the plane.