Precalculus- finding torque using cross products?

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There is an example problem too, it didn't help me, but I'll it for reference:
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1 Answer
Jun 6, 2018

Taking +x+x-axis towards east, +y+y-axis towards north and +z+z-axis out of the paper with location where ratchet is fixed on the nut as origin of coordinates.
Using similar figure as given in the example.

Applied force is vecF =-42hatj\ N
The radius vector for calculation of torque can be resolved in its components as vecr=(-0.59cos38^@hati-0.59sin 38^@hatj)\ m

Torque vectau=vecrxxvecF
Inserting above values we get

vectau=(-0.59cos38^@hati-0.59sin 38^@hatj)xx(-42hatj)
=>vectau=(-0.59cos38^@hati)xx(-42hatj)
=>vectau=19.5hatk\ Nm
=>|vectau|=19.5\ Nm