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Find the torque of a force 7 hat(i) + 3 ...

Find the torque of a force `7 hat(i) + 3 hat(j) - 5 hat(k)` about the origin. The force acts on a particle whose position vector is `hat(i) - hat(j) + hat(k)`

Text Solution

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Given, positon vector
`vec(r) = hat(i) - hat(j) + hat(k)`
Force, `vec(F) = 7 hat(i) + 3 hat(j) - 5 hat(k) , "Torque", tau = ?`
`vec(tau) = vec(r) xx vec(F) = |(hat(i),hat(j),hat(k)),(1,-1,1),(7,3,-5)|`
`= (5 - 3) hat(i) - (-5-7)hat(j) + (3 + 7)hat(k)`
`= 2 hat(i) + 12 hat(j) + 10 hat(k)`
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