# Vectors: cross product question

1. Feb 17, 2008

### tony873004

If a, b, and c are vectors, and a=b x c, and a and c are known, how do I solve for b?

b=a/c ? I don't think we've covered diving vectors, and since the cross-product is a special case of multiplying vectors (as opposed to dot product), I'm not sure this is allowed anyway.

I'm trying to compute dipole moment, given a torque and an electric field. In my above example, a is torque, and c is electric field. I need to solve for b.

Thanks!

2. Feb 17, 2008

### rocomath

We know that a is orthogonal to vector b & c, hence the cross product. So, one way to know if two vectors are orthogonal is proving that the dot product is 0.

Let $$b=<b_1,b_2,b_3>$$

$$b\cdot(b \ x \ c)=0$$

There should be a property and perhaps an example on how to do this operation. If you are unable to find it, let me know and I will show you.

Last edited: Feb 17, 2008
3. Feb 17, 2008

### tony873004

There are similar examples in our notes where we find the torque, but not the dipole moment. At first glance, this looked like an easy problem. I'm a little confused by the direction you're going, since "a" has not been used.

I'm going to change the variables from a b & c to t (torque), p (dipole moment), and E (electric field) just to be consistent. (t is actually tau, but you get the point).
so
t=3.7*10-3
E= 3.7*103 , 30°
solve for p

And from class notes,
t= p x E

4. Feb 17, 2008

### rocomath

What are the points for vectors a & c? And I am using a, it's (b x c).

5. Feb 17, 2008

### tony873004

sorry, I switched the variable names. a became t. b became p, and c became E.
So we bave t = p x E. Solve for p, with t and E given.