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Question:

Given that force (5^i + 7^j - 3^k) N acts on a particle at position (^i + ^j - ^k) m. Find torque of this force on the particle about the origin.

2^i - 3^j + 4^k

4^i - 2^j + 2^k

6^i - 4^j + 4^k

5^i - 2^j + 3^k

Solution:

From the definition of torque, we have:
Torque, τ = r × F = (^i + ^j - ^k) × (5^i + 7^j - 3^k)
= ^i(-3 + 7) - ^j(-3 + 5) + ^k(7 - 5)
τ = 4^i - 2^j + 2^k