1
Question
Find the torque by the force, →F=2^i+3^j+5^k acting at the point →r1=5^i+2^j−^k about the point →r2=6^i−4^j+^k.
Find the torque by the force, →F=2^i+3^j+5^k acting at the point →r1=5^i+2^j−^k about the point →r2=6^i−4^j+^k.
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Solution
The correct option is B 36^i+^j−15^k
Given, force →F=2^i+3^j+5^k
→r=→r1−→r2
=(5^i+2^j−^k)−(6^i−4^j+^k)
=−^i+6^j−2^k
Torque about point →r2 is given by →τ=→r×→F
=(−^i+6^j−2^k)×(2^i+3^j+5^k)
=∣∣
∣
∣∣^i^j^k−16−2235∣∣
∣
∣∣
=^i(30+6)−^j(−5+4)+^k(−3−12)
∴→τ=36^i+^j−15^k
Given, force →F=2^i+3^j+5^k
→r=→r1−→r2
=(5^i+2^j−^k)−(6^i−4^j+^k)
=−^i+6^j−2^k
Torque about point →r2 is given by →τ=→r×→F
=(−^i+6^j−2^k)×(2^i+3^j+5^k)
=∣∣ ∣ ∣∣^i^j^k−16−2235∣∣ ∣ ∣∣
=^i(30+6)−^j(−5+4)+^k(−3−12)
∴→τ=36^i+^j−15^k
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