1
Question
A force →F=3^i+2^j−4^k acts at the point (1,−1,2). Find its torque about the point (2,−1,3).
A force →F=3^i+2^j−4^k acts at the point (1,−1,2). Find its torque about the point (2,−1,3).
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Solution
The correct option is B 2^i−7^j−2^k
Here, →F=3^i+2^j−4^k is acting at a point (1,−1,2)
⇒→r=(1−2)^i+(−1−(−1))^j+(2−3)^k=−^i−^k
Hence torque about point (2,−1,3) :
→τ=→r×→F
→τ=(−^i−^k)×(3^i+2^j−4^k)
→τ=∣∣
∣
∣∣^i^j^k−10−132−4∣∣
∣
∣∣
→τ=^i(2)−^j(4+3)+^k(−2)
→τ=2^i−7^j−2^k
Here, →F=3^i+2^j−4^k is acting at a point (1,−1,2)
⇒→r=(1−2)^i+(−1−(−1))^j+(2−3)^k=−^i−^k
Hence torque about point (2,−1,3) :
→τ=→r×→F
→τ=(−^i−^k)×(3^i+2^j−4^k)
→τ=∣∣ ∣ ∣∣^i^j^k−10−132−4∣∣ ∣ ∣∣
→τ=^i(2)−^j(4+3)+^k(−2)
→τ=2^i−7^j−2^k
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