If any problem involving circular motion, which way does the acceleration vector point ?

The acceleration vector always points towards the centre of the motion. This is referred to as centripetal acceleration. It accounts for the centripetal force that tends to pull the object in circular motion towards the centre of motion.

Consider the diagram below;

it illustrates a body in circular motion along the black circle, with the acceleration vector a shown by the orange arrow pointing towards the centre of motion and the velocity vector v shown by the green arrow pointing tangentially away from the circumference.

6 cos 34, 6 sin 34 trig

a straight line sloped