How to calculate torque with cross product?

[mohemoto]

Homework Statement

A rod has one end at the origin and one end at the point P whose coordinates are (1m, 2m, 2m). A force F = (3i+2j-1k) N acts on the rod at the point P. What is the torque about the origin due to F?

Homework Equations

torque = F x r

The Attempt at a Solution

I'm not sure what to multiply by what. Are there any suggestions?

 

[rock.freak667]

Well what is the vector OP which is the same as your vector r?

 

[collinsmark]

Use the definition of cross product. (If it's still unclear, do an internet search on "determinant of a matrix.")

$$\vec a \times \vec b = <br /> \left|<br /> \begin{array}{ccc}<br /> \hat \imath & \hat \jmath & \hat k \\<br /> a_x & a_y & a_z \\<br /> b_x & b_y & b_z<br /> \end{array} <br /> \right|$$

 

[PhanthomJay]

Since the force is already given in mutually perpendicular directions x , y, and z, (i, j, and k unit vectors), then use Torque = force times perpendicular distance from line of action of force to the axis about which you are summing moments.
T_x = F_y(z) + F_z(y)
T_y = F_z(x) + F_x(z)
T_z = F_y(x) + F_x(y)

Please watch plus and minus signs. By convention, counterclockwise moments about an axis are taken as positive (x axis points right positive, y-axis points up positive, and z axis points out of plane toward you as positive).