# Find a plane given a point and a parallel line

1. Sep 14, 2011

### Latecomer

1. The problem statement, all variables and given/known data

Find the equation of the plane through the point (-2,8,10) and parallel to the line x= -2+t, y= 1+2t, z= 4-3t.

2. Relevant equations

3. The attempt at a solution

Now, I understand that I have to find the normal vector to the line (and the plane), but how can I do that if I only have one directional vector? If I had another directional vector, I could use the cross product.
I understand that the line has directional vector of (1,2,-3). Is there a way to get the normal vector through this information alone? Maybe by finding the orthogonal vector through the dot product or something (can you do that)?
If I have enough information to find the normal vector, would having only one point on the plane give me enough information to get the equation of the plane?

Thanks for your time, I'm having trouble here.

2. Sep 14, 2011

### Tomer

This is obviously not enough information, since I could easily draw two different planes going through a given point a parallel to a certain line (try it yourself).

Maybe they mean that the normal is parallel to the line? Then it is enough information of course...

3. Sep 14, 2011

### Latecomer

I'm not sure what he wants. This is a question on a practice test that the professor made up himself- the questions aren't out of any book or anything.
When I asked him about the question, I insisted that I needed another point or something, but he said that the information was all there and that's all that I got out of him.

The question shown is exactly how it's stated, though. Unless, like you said, it's just badly worded?

4. Sep 14, 2011

### Tomer

Well, as I've said, I could draw a lot of planes parallel to the given line and passing through the point. I can only guess he meant the normal being parallel to the line. Otherwise send your prof here :-)