Given two vectors $\overrightarrow{e}$ and $\overrightarrow{f}$ as shown in Figure 2, what is the angle $\pi$ between them if $\overrightarrow{e}$ points along the positive x-axis and $\overrightarrow{f}$ points along the positive y-axis?

• A. $45°$
• B. $0°$
• C. $180°$
• D. $90°$

Answer: (D)

Verified step by step guidance

1. Identify the directions of the two vectors: vector \( \vec{e} \) points along the positive x-axis, and vector \( \vec{f} \) points along the positive y-axis.
2. Recall that the positive x-axis and positive y-axis are perpendicular to each other in a standard Cartesian coordinate system.
3. Understand that the angle \( \pi \) between two vectors is the measure of the smallest rotation from one vector to the other.
4. Since \( \vec{e} \) is along the x-axis and \( \vec{f} \) is along the y-axis, the angle between them is the angle between the x and y axes, which is \( 90^\circ \).
5. You can also confirm this by using the dot product formula: \( \vec{e} \cdot \vec{f} = |\vec{e}| |\vec{f}| \cos(\pi) \). Since the dot product is zero for perpendicular vectors, \( \cos(\pi) = 0 \), which implies \( \pi = 90^\circ \).