Force f with arrow = (9.0 n)i hat − (9.0 n)k acts on a pebble with position vector r with arrow = (0.90 m)j − (1.2 m)k relative to the origin. in unit-vector notation, what are the following? (a) the resulting torque on the pebble about the origin

τ = - (8.1 N-m) i - (10.8 N-m) j - (8.1 N-m) k

Explanation:

Given

r = (0 m) i + (0.9 m) j - (1.2 m) k

F = (9 N) i + (0 N) j - (9 N) k

We can apply

τ = r x F

τ = ((0 m) i + (0.9 m) j - (1.2 m) k) x ((9 N) i + (0 N) j - (9 N) k)

⇒  τ = - (8.1 N-m) i - (10.8 N-m) j - (8.1 N-m) k

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