# If work is zero, when is force nonzero?

Force and displacement are perpendicular each other when work done is zero.

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Normally, when we talk about force and displacement, we refer to the definition of work in a one-dimensional representation:

where work is negative with respect to the worker who is say, pushing a box.

On the other hand, if we imagine a force entirely perpendicular to the desired displacement, there is no component of the force that causes the displacement.

So, I don't think such a force is nonzero.

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Force is nonzero when there is a displacement occurring against a resisting force, but the angle between the force and displacement vectors is such that the component of force in the direction of displacement is zero.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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