A point of application of a force F→=4i^−5j^+3k^ is moved from r→0=i^+2j^+3k^ . The torque about a point r→=3i^−2j^−3k^ is:
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a
42i^+30j^−6k^
b
Zero
c
42i^+30j^+6k^
d
42i^−30j^+6k^
answer is A.
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Detailed Solution
Torque acting about a point P [ Position vector of point P is P→ (say)] due to force F→ is given byτ→=P→×F→P→=r→0−r→=(i^+2j^+3k^)−(3i^−2j^−3k^)=−2i^+4j^+6k^τ→=(−2i^+4j^+6k^)×(4i^−5j^+3k^)=i^(12+30)−j^(−6−24)+k^(10−16)=42i^+30j^−6k^