How Do You Calculate Torque from Cross Product?

[Nanuven]

Force F = (9.0 N) i hat + (-4.0 N) k hat acts on a pebble with position vector r = (3.00 m) j hat + (-1.0 m) k hat, relative to the origin.(a) What is the resulting torque acting on the pebble about the origin?
( N·m) i hat + ( N·m) j hat + ( N·m) k hat

(b) What is the resulting torque acting on the pebble about a point with coordinates (0.0 m, 0.0 m, 5.0 m)?
( N·m) i hat + ( N·m) j hat + ( N·m) k hat
So all I could come up with was cross product was that torque = r cross F

Therefore T = fRsin$$\theta$$

I looked up cross product on Wikipedia (not best site I know but w/e) and it came up with:

i x j = k
j x k = i
k x i = j

I tried those but it doesn't seem to be giving me the right answer. Any help please??

The Attempt at a Solution

 

[Mentz114]

$$F = \[ \left[ \begin{array}{c} 9 \\\ 0 \\\ -4 \end{array} \right]\]$$

$$R = \[ \left[ \begin{array}{c} 0 \\\ 3 \\\ -1 \end{array} \right]\]$$

$$F \times R = \[ \left[ \begin{array}{c} F_2R_3-F_3R_2 \\\ F_3R_1-F_1R_3 \\\ F_1R_2-F_2R_1 \end{array} \right]\]$$

$$F \times R = \[ \left[ \begin{array}{c} -12 \\\ -9 \\\ -27 \end{array} \right]\]$$

I did this with software. I haven't hand checked it.

 

[tiny-tim]

torque = r cross F

i x j = k
j x k = i
k x i = j

Hi Nanuven!

Also ii = jj = kk = 0.

Treat cross products just the same as any product.

For example:

(ai + bj)(cj + dk)

= acij + adik + bcjj + bdjk

= ack - adj + bdi.

(btw, use the B tag to do bold … if that doesn't work, type [noparse] before and after.[/noparse])