Thread: Plane and a line

1. 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.

2. 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) $n \cdot V = 0$, the normal and direction vector are perpendicular.

b) $V = \alpha n$, the direction vector is parallel to the normal.

c) $n \cdot V \ne 0\;\& \;p(t) \not\subset U$

3. Just thought I'd point out that for c), if $n \cdot V \ne 0\;$, then you already know that $\;p(t) \not\subset U$, since the normal vector would be perpendicular to any line in the plane.