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## Main Question or Discussion Point

I was going through my basic definitions of postion (in terms of paths), velocity, and speed. The problem Im running into is this:

if you can prove by definition of dot product when velocity is perpendicular to the postion function and that velocity exists, does this mean speed is perpendicular to the position function as well.

So far I just proved to my self that if the angle is 90, cos(90) gives 0, and thus dot product of the postion and velocity is zero. Can the dot product be applied to speed to show speed is perpendicular as well?

if you can prove by definition of dot product when velocity is perpendicular to the postion function and that velocity exists, does this mean speed is perpendicular to the position function as well.

So far I just proved to my self that if the angle is 90, cos(90) gives 0, and thus dot product of the postion and velocity is zero. Can the dot product be applied to speed to show speed is perpendicular as well?