State whether the following statements are true or false:
$(a)$ If the angular velocity is constant on a circular path,the linear velocity is also constant.
$(b)$ In projectile motion,the velocity vector of the projectile is always perpendicular to the acceleration vector.
$(c)$ For the maximum horizontal range $R$ of a projectile,the maximum height attained is $\frac{R}{4}$.
$(d)$ If $|\vec{A} \times \vec{B}| = AB$,then the angle between $\vec{A}$ and $\vec{B}$ is zero.

(C) False. In uniform circular motion,the magnitude of linear velocity is constant,but its direction changes continuously.
$(b)$ False. The velocity vector is perpendicular to the acceleration vector only at the highest point of the trajectory.
$(c)$ True. For maximum range,the angle of projection $\theta = 45^{\circ}$. The maximum height $H = \frac{u^2 \sin^2 \theta}{2g} = \frac{u^2 \sin^2 45^{\circ}}{2g} = \frac{u^2}{4g}$. The range $R = \frac{u^2 \sin 2\theta}{g} = \frac{u^2}{g}$. Thus,$H = \frac{R}{4}$.
$(d)$ False. If $|\vec{A} \times \vec{B}| = AB$,then $AB \sin \theta = AB$,which implies $\sin \theta = 1$,so $\theta = 90^{\circ}$.