Product of a vector and its derivative

[Glom]

r.v = rv

That's what this book says, but I don't buy it.

If v were tangential to r, the dot product would be zero. But product of their magnitudes could still easily be non-zero.

[grapes]

r.v = rv

That's what this book says, but I don't buy it.

If v were tangential to r, the dot product would be zero. But product of their magnitudes could still easily be non-zero.

Which derivative are they using?

[tusenfem]

The dot product as you write it up there is defined as:

v•r = v r cos(θ)

where the bold are vectors and the non-bold v and r are the magnitude of the vectors and θ is the angle between v and r.

Now we know that there is a relationship between v and r namely that v = dr/dt, velocity is the temporal derivative of the location vector. So now we get:

v•r = dr/dt•r, but still that will not delete the cos(θ), only when the body is moving in a rectilinear direction.