# Angle between intersecting vectors

1. Feb 9, 2013

### Reefy

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

Given 2 lines, determine whether they are intersecting or not. If they are, determine the angle between them.

Line(1): x = 1-t, y = 3-2t, z = t
Line(2): x = 2+3t, y = 3+2t, z = 1+t

2. Relevant equations

cos(theta) = (a·b)/($\left|a\right|$$\left|b\right|$)

3. The attempt at a solution
I know that they intersect, I've done all the work in my notebook and checked the back of the book for the answer and they indeed intersect. My problem lies with finding the angle.

Since I have those two lines up above, doesn't that mean I can find the direction vectors of both and both direction vectors will intersect with the same angle as the lines? If so, I tried using the above equation with

a = <-1,-2,1> and b=<3,2,1>

and I am unable to get 49.1° which is the answer.

2. Feb 9, 2013

### Dick

All looks right so far. What do you get for the answer? I think the answer to your dilemma is that e.g. some people would consider an angle of 170° to be the same as angle of 10° if you aren't paying attention to the direction of the vectors. Just to the angle between them.

3. Feb 9, 2013

### Reefy

Ah, that might be it. I remember my professor saying something along those lines.

arccos(-6/√84) ≈ 130.9°

Edit: The thing you were saying at the end, can you explain it a little? I think you're right because if I subtract 130.9 from 180, I get 49.1 degrees. But why do I need to subtract it from 180?

4. Feb 9, 2013

### Dick

Because if you are measuring the angle between two lines you might interpret it to be acute angle between them. I actually think the answer 130.9 is the better answer because vectors do have a direction. But what if your professor says 'angle' means that you'd better go along.

5. Feb 9, 2013

### Reefy

Ah, ok. It kinda makes senses. I'm gonna ask my professor which answer he would prefer.

Thanks for the help!