1. ## Vector help!

Alright, so I have two questions actually on the same subject. The first is:

The figure shows a vector a in the xy-plane and a vector b in the direction of k. Their lengths arc |a|=3 and |b|=2. Find |a x b|.

I know the equation is |a x b| = |a||b|sin(theta) but I can't figure out how to find theta. I've looked up solutions for the problem and people keep saying pi/2. I just don't know how they are coming up with this!!! Help?

The second is:

Show that (a x b) dotted with b = 0 for all vectors a and b in Vsub3.

I'm not good at the math symbols so yeah. Sorry it's not really easy to read but I can't figure out what exactly to do for this. I'm not too good with proving something. Any help appreciated!

Thanks,
Cen

2. Originally Posted by Centara
The figure shows a vector a in the xy-plane and a vector b in the direction of k. Their lengths arc |a|=3 and |b|=2. Find |a x b|.
The vector k is perpendicular to any line which is a subset of the xy-plane.

3. Thank you!

Any advice on the second one?

4. Originally Posted by Centara
Any advice on the second one?
By definition $\displaystyle a \times b$ is a vector that is perpendicular to both a & b.