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If a force ⃗F=3̂i+4̂j-2̂k acts on a particle having position vector 2̂i+̂j+2̂k, then the torque about the origin will be

Asked in JEE Main 25th June 1st Shift 2022 · Torque and moment of a force

• (1) 3̂i+4̂j-2̂k
• (2) -10̂i+10̂j+5̂k
• (3) 10̂i+5̂j-10̂k
• (4) 10̂i+̂j-5̂k

Step-by-step solution

Why the other options are wrong

• (1) comes from this is the force itself, copied across. Torque is ⃗r×⃗F; it can never be equal to ⃗F, because it is perpendicular to it.
• (3) comes from the right three numbers in the wrong places. Sanity check: (10,5,-10)·(3,4,-2)=30+20+20=70 eq0, so it is not perpendicular to ⃗F.
• (4) comes from sanity check: (10,1,-5)·(2,1,2)=20+1-10=11 eq0, so it is not perpendicular to ⃗r either.

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