Thread: Plane and a line

Let U be a plane given by the point x and the normal vector n.

Suppose that p(t) = y + Vt be the parametric equation of the line l. Find condition on U and l such that:

a) U || l
b) l perpendicular U
c) l intersects U at a single point, find the point.

Should I start by finding a line in U? And how do I do it?

I'm sorry, I'm really lost on this one here, because the professor can't speak any English.

Originally Posted by tttcomrader

Let U be a plane given by the point x and the normal vector n. Suppose that p(t) = y + Vt be the parametric equation of the line l. Find condition on U and l such that:
a) U || l
b) l perpendicular U
c) l intersects U at a single point, find the point.

a) , the normal and direction vector are perpendicular.

b) , the direction vector is parallel to the normal.

c)

Just thought I'd point out that for c), if , then you already know that , since the normal vector would be perpendicular to any line in the plane.