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Torque is defined as a measure of how much a force acting on an object causes that object to rotate. The object rotates about an axis, which is called the pivot point. Let the force acting on it is 'F'. The distance from the pivot point to the point where the force acts is called the moment arm, and is denoted by 'r'.
Now, torque, τ = r * F = rFsin Ѳ
Hence, torque is the cross product between the distance vector (the distance from the pivot point to the point where force is applied) and the force vector, 'a' being the angle between r and F. We are taking cross product because the variables involved are vectors. Note that the distance in this case is a vector.
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