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What is the torque of the force ⃗F=2̂i-3̂j+4̂k N acting at the point ⃗r=3̂i+2̂j+3̂k m about origin?

Asked in CBSE AIPMT 1995 · Torque and moment of a force

• (1) -6̂i+6̂j-12̂k
• (2) -17̂i+6̂j+13̂k
• (3) 6̂i-6̂j+12̂k
• (4) 17̂i-6̂j-13̂k

Step-by-step solution

Why the other options are wrong

• (1) comes from multiplying the components straight through, 3×2=6, 2×(-3)=-6, 3×4=12, and then flipping the signs, instead of forming the cross product
• (2) comes from the right three magnitudes with every sign reversed, which is ⃗F×⃗r rather than ⃗r×⃗F
• (3) comes from the component-wise product again, this time with the signs left alone

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