# I need help evaluating this vector product identity

1. Sep 8, 2008

### sunnyslumber

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

The problem is written as:

Del X (A X B) = (B*DEL)A- (A*DEL)B +A(DEL*B) -B(DEL * A)

where * = dot. I don't know how to evaluate this because if the author meant for the standard mathematical order of operations to apply it makes since they wouldn't have worried about the sequence of the statements (since the dot product iscommutative). Every way I'm working it its coming up wrong.

Can anyone help? I just need to know how to evaluate the expression.

2. Relevant equations

3. The attempt at a solution

Last edited: Sep 8, 2008
2. Sep 8, 2008

### edziura

I assume that what you've been ask to do is to prove this vector identity, which is what it is. There are at least two ways to do this, perhaps three. The simplest way, and one which is independent of any particular coordinate system, is to use tensor notation ( a vector is a tensor of rank 1), but I'm guessing you are not familiar with tensors.

Another much more tedious method is to prove its true in the rectangular coordinate system; this doesn't make it necessarily true for vectors in general, but it may suffice for your purposes. Basically what your do is start by expanding both sides. Then sum all the x components on the right side, and you'll see that the resulting x components are the same on both sides. Then wave your arms wildly and say that by the same process, the y and z components are equal (which they are), or continue the tedium if you must.

All this assumes you know how to expand each of the five vector terms.