Find Line in Plane Passing Through (2,3,6)

[dtl42]

Homework Statement

Given some plane, $$3x+2y-z=6$$, and a point $$(2,3,6)$$

Find a line in the plane passing through that point.

Homework Equations

The Attempt at a Solution

I tried finding the vector perpendicular to the plane, $$<3,2,-1>$$, but I'm not sure what to do with it.

 

[jeffreydk]

A line passing through two points $\vec{r_0}$ and $\vec{r_1}$ is simply

$$\vec{r}=(1-t)\vec{r_0}+t\vec{r_1}$$

You are given a point that you want the line through and you can figure out another arbitrary one right?

 

[rock.freak667]

I tried finding the vector perpendicular to the plane, $$<3,2,-1>$$, but I'm not sure what to do with it.

You could use this as the direction of the line that you want.


EDIT: Read the question wrong, I thought it asked for a line passing through that point and not necessarily contained in the plane.

 

[HallsofIvy]

No, you cannot! That vector is perpendicular to the plane while the line you want is in the plane. The normal vector doesn't help at all. As jeffreydk said, a line is determined by two points. You are already given one point in the plane (did you check that it actually is in the plane?) Now choose any other point in the plane (take what ever values you like for x and y and solve for z) and use those two points to determine the line. There are, of course, an infinite number of solutions.