Question

A force F=(2hati+3hatj-2hatk)N is acting on a body at point (2m, 4m,-2m). Find torque of this force about origin.

Answer 1

torque of this force about origin = -2i - 2k

given, A force = (2i + 3j - 2k) N is acting on a body at point (2, 4, -2).

we have to find torque of this force about origin.

we know, $\bf{\vec\tau=\vec r\times\vec F}$

τ = {(2 - 0)i + (4 - 0)j + (-2 - 0)k} × (2i + 3j - 2k)

= (2i + 4j - 2k) × (2i + 3j - 2k)

= i(4 × -2 - 3 × -2) - j(2 × -2 -2 × -2) + k(2 × 3 - 4 × 2)

= i (-8 + 6) - j (-4 + 4) + k(6 - 8)

= -2i - 2k

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