# Product of vector

1. Sep 6, 2011

### hpysm

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

The vectors A, B and C have components Ax = 3, Ay = -2, Az = 2, Bx = 0, By = 0, Bz = 4, Cx = 2, Cy = -3, Cz = 0. Calculate the A X (B + C) ??

2. Relevant equations

3. The attempt at a solution

2. Sep 6, 2011

### lanedance

hey hypsm - where are you stuck?

evaluate B+C first

3. Sep 6, 2011

### hpysm

I am ding this way: A X (B + C)=AXB+AXC = AXBsin(x) + AXCsin(x); how I can get angle of x degree ?

4. Sep 6, 2011

### SteamKing

Staff Emeritus
Don't you know how to calculate a cross product using the components of the two vectors? BTW, lanedance's suggestion will save you some calculating, since the addition of two vectors first is much simpler than taking two cross products and then adding.

5. Sep 6, 2011

### lanedance

that doesn't quite make sense... AXB is a vector and the magnitude is given by
|AXB| = |A|.|B|sin(x).n

where n is a unit vector perpendicular to both A & B, and x is the angle between them.

the angle between A and B, will not in general be the same as that between A and C, neither will thr normal vector.

Hence I would do it the way first suggested... (evaluate B+C first)

however, if you want to keep going your way it should be
A X (B + C)=A X B+ AX C = n|A|B||sin(x) + m|A||C|sin(y)

one good way to find the angel is using the dot product..

if you were just looking to find the magnitude of the vector this would all simplify

6. Sep 7, 2011

### HallsofIvy

If $\vec{A}= A_x\vec{i}+ A_y\vec{j}+ A_z\vec{k}$ and $\vec{B}= B_x\vec{i}+ B_y\vec{j}+ B_z\vec{k}$ then, symbolically,
$$\vec{A}\times\vec{B}= \left|\begin{array}{ccc}\vec{i} & \vec{j} & \vec{k} \\ A_x & A_y & A_z \\ B_x & B_y & B_z \end{array}\right|$$

You really need to know that before you can do this problem.