# Speed and Velocity in relation to Postition

## 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?

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In short, speed is not a vector. If v is a scalar, and w is not, it makes no sense to dot v and w. Geometrically, speed is the length of the velocity vector.

For something to chew on, consider the following:

In one dimensional motion, say constrained to the x-axis, then if velocity is perpendicular to position, then (x,0,0)$\cdot$(v,0,0)=xv=0 implies x or v is zero.

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Can the dot product be applied to speed to show speed is perpendicular as well?
It's not (only) that the dot product cannot be applied to speed to find the angle.
The expression "speed is perpendicular" does not make sense to start with. Speed is a scalar so does not have a direction associated.