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Here is an excerpt that is provided me with confusion:

"The total linear momentum [itex]\vec{p}[/itex] of a particle is conserve when the total force on it is zero

Note that this result is derived from the vector equation [itex]\vec{p} = \vec(0}[/itex], and therefore applies for each component of the linear momentum.

**To state the result in other terms, we let [itex]\vec{s}[/itex] be some constant vector such that [itex]\vec{F} \cdot \vec{s} = \vec{0}[/itex]indepent of time. Then [itex]\vec{p} \cdot {s} = \vec{F} \cdot \vec{s} = \vec{0}[/itex] or, integrating with respect to time [itex]\vec{p} \cdot \vec{s} = c[/itex] which states that the component of linear momentum in the direction in which in the force vanishes is constant in time**

The part in bold is particularly confusing. Could someone help, please?