How do I determine the magnitude of torque from a cross product?

[smatt_31]

[SOLVED] the magnitude of torque

Homework Statement

Determine the magnitude of the torque about A by evaluating lABxFl (the magnitude of vector AB cross vector F) where AB = -15i + 12j and F= -200lbs (cos theta)i - 200lbs (sin theta)j

Homework Equations

cross product and maybe the magnitude of torque

The Attempt at a Solution

so i did the cross product and ended up with
k = (-15(-200 sin theta))-(12(-200cos theta)) whick i simplified
to 3000(sin theta) + 2400(cos theta)

so k = 3000(sin theta) + 2400(cos theta)

so am I done or should I take the sqrt of the values = to k ??
the problem i have with this is theta is undefined and i would end up with a more complicated expression.
so what do i do

 

[HallsofIvy]

Homework Statement

Determine the magnitude of the torque about A by evaluating lABxFl (the magnitude of vector AB cross vector F) where AB = -15i + 12j and F= -200lbs (cos theta)i - 200lbs (sin theta)j

Homework Equations

cross product and maybe the magnitude of torque

The Attempt at a Solution

so i did the cross product and ended up with
k = (-15(-200 sin theta))-(12(-200cos theta)) whick i simplified
to 3000(sin theta) + 2400(cos theta)

so k = 3000(sin theta) + 2400(cos theta)

so am I done or should I take the sqrt of the values = to k ??
the problem i have with this is theta is undefined and i would end up with a more complicated expression.
so what do i do

That is not "k= ". What you have is the coefficient of k (unit z-vector). The magnitude is the value of that coefficient. If you wanted to be real technical, the "magnitude" is the square root of the square of that: its absolute value and so just what you have as long as it is positive.