Given two vectors $\overrightarrow{e}$ and $\overrightarrow{f}$ shown in Figure 1, what is the angle $\theta$ between them if $\overrightarrow{e}$ points along the positive $x$-axis and $\overrightarrow{f}$ points along the positive $y$-axis?

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

Answer: (A)

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. Use the definition of the angle \( \theta \) between two vectors, which can be found using the dot product formula: \[ \vec{e} \cdot \vec{f} = |\vec{e}| |\vec{f}| \cos(\theta) \]
4. Since \( \vec{e} \) and \( \vec{f} \) are along the x and y axes respectively, their dot product is zero because they have no components in common, implying \[ \cos(\theta) = 0 \]
5. Solve for \( \theta \) by taking the inverse cosine of zero, which corresponds to the angle between the two vectors.