In unit-vector notation, what is the torque about the origin on a particle locat

Question

In unit-vector notation, what is the torque about the origin on a particle located at coordinates (0 m, -3.0 m, 2.0 m) due to force F_1^vector with components F_1x = 5.0 N and F_ly = F_1z = 0? Tau^vector = 15k + 10J N middot m In unit-vector notation, what is the torque about the origin on a particle located at coordinates (0 m, -3.0 m, 2.0 m) due to force F_2^vector with components F_2x = 0, F_2y = 3.0 N, and F_2z = 5.0 N? tau^vector = -21i N middot m Torque is the cross product of a position vector (extending from a chosen point, here the origin, to the particle) and a force vector

Explanation / Answer

F = F1x i + F1y j + F1z k = 5i

position r = 0i - 3j + 2 k

torque = r x F

torque = (3j + 2k) x 5i

torque = (3*5)*(jxi) + (2*5)(kxi)

torque = -15k + 10 j

torqu = 10j - 15 k Nm   <<------answer

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(b)

F2 = F2x i + F2y j + F2z k = 3j + 5 k

position r = 0i - 3j + 2 k

torque = r x F

torque = (3j + 2k) x (3j + 5k)

torque = (3*3)*(jxj) + (3*5)(jxk) + (2*3)*(kxj) + (2*5)(kxk)

torque = 9*0 + 15 i - 6 i + 10*0

torque = 9i Nm   <<------answer

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