ABCDEF is a regular hexagon in which AB represents vector p and BC represents vector q.Find what CD,DE,EF & FA represent in terms of vector p and vector q.

Since opposite vectors in a regular hexagon are equal in magnitude and direction,

AB = ED = p

BC = EF = q

The sum of the interior angles of a polygon = (n-2) * 180°

and any one interior angle is, (n-2)/n * 180°

therefore, angle ABC is (6-2)/6 * 180° = 120°

Now, AF is resolved into two vectors, -p and q sin 30°

hence, AF = -p + q sin 30°

similarly, CD = -p + q sin 30°