Question

In hinge joints, a pair of muscles is arranges on the same plane as that of the joint while in ball and socket joints, at least two pairs of muscles are present perpendicular to each other.
Please explain.

Answer 1

Think about the purpose of the joints.
Hinge joints have one range of motion. For example, the elbow joint can only bring the lower arm in towards the upper arm or away from it. This means that it only needs one pair of flexor/extensor muscles to complete its range of motion.
Ball and socket joints have multiple ranges of motion, so require multiple muscles to encompass those ranges.

Remember skeletal muscle is striated, so it only contracts along its horizontal axis.

Answer 2

But what is meant by planar or perpendicular arrangement of muscles?

Answer 3

Don't quote me on this, but I think it means the direction of the muscle in relation to the joint. Planar would mean running along the same plane or direction of the hinge, while perpendicular means running at an angle from the hinge. So for example at the elbow you have the bicep (flexor) muscle and the tricep (extensor) muscle. They run along the same plane as the hinge, so they are planar muscles.