Question

# Two forces −→F1=2^i−5^j−6^k and −→F2=−^i+2^j−^k are acting on a body at a point (1,1,0) and (0,1,2) respectively. Find the torque acting on the body about the point (−1,0,1).

A
14^i+10^j9^k
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B
11^i+10^j12^k
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C
3^i+3^k
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D
14^i10^j9^k
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Solution

## The correct option is A −14^i+10^j−9^k From the diagram, →r1=(1−(−1))^i+(1−0)^j+(0−1)^k →r1=2^i+^j−^k........(I) →r2=(0−(−1))^i+(1−0)^j+(2−1)^k →r2=^i+^j+^k.....(II) As we know, →τ=→r×→F →τ1=→r1×−→F1 →τ1=∣∣ ∣ ∣∣^i^j^k21−12−5−6∣∣ ∣ ∣∣ →τ1=i(−6−5)−j(−12+2)+^k(−10−2) =−11^i+10^j−12^k And →τ2=→r2×−→F2 →τ=∣∣ ∣ ∣∣^i^j^k111−12−1∣∣ ∣ ∣∣ →τ2=^i(−1−2)−^j(−1+1)+^k(2+1) →τ2=−3^i+3^k Therefore, net torque about point (−1,0,1) is →τ=→τ1+→τ2 →τ=−11^i+10^j−12^k−3^i+3^k →τ=−14^i+10^j−9^k

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