a. What is the angle Φ between vectors E and F in FIGURE P3.24?

Key Concepts

Vector Representation

Vectors are quantities that have both magnitude and direction, represented graphically as arrows. The length of the arrow indicates the vector's magnitude, while the arrowhead shows its direction. In the context of the question, vectors E and F are represented in a coordinate system, allowing for the analysis of their relationship through the angle between them.

Angle Between Vectors

The angle between two vectors can be determined using the dot product formula, which relates the cosine of the angle to the magnitudes of the vectors and their dot product. This angle is crucial for understanding how the vectors interact, such as whether they are parallel, perpendicular, or at some other angle. In the given figure, the angle Φ represents this relationship between vectors E and F.

Coordinate System

A coordinate system provides a framework for locating points in space using numerical values. In two-dimensional space, points are defined by their x and y coordinates. The figure illustrates vectors in a Cartesian coordinate system, which helps visualize their directions and the angle between them, facilitating the calculation of the angle Φ.