Sorry for the confusion everybody, I was just trying to show that one side of 3.) is equal to the other side.
My solution (attached to the original problem) used the definition of the dot product and the fact that the angle between r and v is 0 (both pointed out by delta!) I just want to make...
1.)##\dot{\vec{r}}=\dot{x}\hat{i}+\dot{y}\hat{j}+\dot{z}\hat{k}=\dot{r}\hat{r}## since the unit vector is constant
2.) ##\dot{r}\hat{r}=\frac{x\hat{i}+y\hat{j}+z\hat{k}}{\sqrt{x^2+y^2+z^2}}\frac{\dot{x}x+\dot{y}y+\dot{z}z}{\sqrt{x^2+y^2+z^2}}##...