# Homework Help: Planes in 3 space

1. Oct 1, 2012

### Aliboy

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

A plane is perpendicular to the line given by x=3+6t, Y=7+4t, and z=7-9t. What are the components of the normal to the plane

2. Relevant equations

3. The attempt at a solution
I don't understand what the question is asking me all I have figured out that the normal should be parallel to the perpendicular line, but I can't find the normal from the parametric.

2. Oct 1, 2012

### Dick

You can find the tangent vector to the parametric, right? What is it? Then sure, that should be parallel to the normal. Do you want a unit normal vector?

3. Oct 1, 2012

### Aliboy

The only thing I don't understand is finding the tangent vector, all my book and teacher have told me is how to find the vector orthogonal to the plane.

4. Oct 1, 2012

### Dick

The tangent vector to the parametric curve (x(t),y(t),z(t)) is the derivative with respect to t of that. It's (x'(t),y'(t),z'(t)). What is that?

5. Oct 1, 2012

### Aliboy

So 6,4,-9?
So the answer would be <6,4,-9>

6. Oct 1, 2012

### Dick

That's a normal vector to your plane alright. Any multiple of that is also a normal, yes? Do they want any specific one? That's why I asked if you want a 'unit normal'.

7. Oct 1, 2012

### Aliboy

I guess that should do I just don't understand the conceptual behind it.

8. Oct 1, 2012

### Dick

When you said, "I have figured out that the normal should be parallel to the perpendicular line" then that pretty much sums it up. Finding a vector tangent to the perpendicular line will then give you a normal. Just as you did.

9. Oct 1, 2012

### Aliboy

Thank you very much it actually makes sense now.

10. Oct 2, 2012

### HallsofIvy

Part of your problem is shown here:
A plane doesn't have "the tangent vector". Every line in the plane gives a tangent vector. A plane is completely determined by a single point and a vector normal to the plane.