Torque about P (Cross Product?)

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Homework Statement



Textbook figure of a lug wrench on a wheel hub: an 18-in wrench handle with point P at the hub, a 50 lb force arrow at 60 degrees to the handle, and a 9 in distance marked from P to the force line.



Homework Equations



The book says that

Torque = the length of the moment arm X the magnitude of the vertical component of F
= r X F

The Attempt at a Solution



My problem is that I don't have any vectors to do a cross product. Instead I tried to just multiply what I know:

50lbs x 9in x sin60° ≈ 389.71ft-lb

which is far from the correct answer, 32.5ft-lb. The problem seemed simple enough so am I making some small mistake or going about this completely wrong?
 
Just because you aren't given any explicit vectors doesn't mean you can't formulate your own.

Looking at the problem, suppose that we set up an x-axis along the wrench.
In this case, vector r is (9,0) inches, with the emphasis on inches

The force vector F is going to be (50 cos (-60), 50 sin (-60)) lbs.

You can then evaluate r x F in the usual manner

Remember: in x lbs is not equal to ft-lbs
 
Ah, you're right! Thank you, that makes perfect sense.