# Advanced vector question incl. parallelepiped

1. Sep 15, 2010

### agentnerdo

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

Given the three vectors A = 2i + j, and B= i + k, C=4j, find the following

a) |A X B|
b) |A x (B X C)|
c) the volume of the parallelepiped whos concurrent edges rae represented by A B C.

3. The attempt at a solution

I am stuck on A.

I assume it couldnt be as simple as |(2i+j)(i+k)|?
Once I get the first part I will try b and c myself before asking for more help (which I def will need)

2. Sep 15, 2010

### Rasalhague

You need some basic definitions before tackling the question. Google "cross product" and "triple scalar product", or if you have a textbook, look them up there. I think the symbol you wrote as X is the cross that denotes the cross product, and I suspect the symbol you wrote as x should really be the dot that denotes the "dot product" (another one to google if you haven't met that yet).

The pipes, those vertical lines, | ... |, in (a) denote what's called the "length", "magnitude" or "norm" of the vector "A cross B". The pipes in (b) denote the "absolute value" of the number "A dot (B cross C)".

3. Sep 16, 2010

### agentnerdo

I think I am kind of getting it.

Most examples online use three numbers (ie =3i, 5j, 6k)

As such you get a nice little box

In this case, we are missing, for B= any j value, does this mean we assume j=1 for b?

this is what I have so far

i j k

2 1 1 (I assume this is 1, since it is not shown)
1 1 1 (made the assumpetion for j again)
1 4 1

Now, looking at i;

1x1 - 4x1 = -3
i 1-1=0
j ---> 4-1=3