Vectors

Using the law of cosines for the resultant of two vectors and , we know the following relation: Given that the angle between and is , we can substitute the values for and solve for . After solving, we find:
Thus, the correct answer is (d).

A displacement vector represents a change in position from an initial point to a final point, and it is defined by both magnitude and direction. The magnitude represents the straight-line distance between the two points, while the direction indicates the straight-line path between them. Displacement is a vector quantity because it has both magnitude (how far) and direction (where to). This distinguishes it from distance, which only considers the total path traveled and does not include directional information.

Hence, the correct answer is (a).