Advanced vector question incl. parallelepiped

[agentnerdo]

Homework Statement

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.

The Attempt at a Solution

I am stuck on A.

I assume it couldn't 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)

 

[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)".

 

[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


therefore, final answer is 0.