classical mechanics - Relative velocity is not the simple difference of individual velocities?

consider the case when car B was moving vertically up, not in the circular fashion. The relative velocity of A wrt B then would be Va-Vb wouldn't it?

why is it that when car be starts moving in the circle, the relative velocity of A wrt B decreases by the value wXr?

Answer

The formula you have written is valid in both cases:

$$\vec {V_{\text{rel}}}=\vec V_A-\vec V_B-\vec{\omega} \times \vec r$$ When car $B$ is moving on a straight line (vertically), the radius of curvature of its path approaches infinity and so its angular velocity approaches zero ($\omega =\frac{v}{\rho}$). Thus, for the case that car $B$ is moving on a straight line; we have $\vec{\omega} \times \vec r=\vec 0$.