WeBWorK Standalone Renderer

Several unit vectors $\vec{r}, \vec{s}, \vec{t}, \vec{u}, \vec{n},$ and $\vec{e}$ in the xy-plane (not three-dimensional space) are shown in the figure.

Using the geometric definition of the dot product, are the following dot products positive, negative, or zero? You may assume that angles that look the same are the same.

1. $\vec{t} \cdot \vec{u}$

2. $\vec{e} \cdot \vec{s}$

3. $\vec{e} \cdot \vec{r}$

4. $\vec{n} \cdot \vec{t}$

5. $\vec{r} \cdot \vec{s}$

6. $\vec{s} \cdot \vec{t}$

7. $\vec{r} \cdot \vec{u}$

8. $\vec{n} \cdot \vec{e}$

(Click on graph to enlarge)

You can earn 10% partial credit for 2 - 4 correct answers, 60% partial credit for 5 - 6 correct answers, and 80% partial credit for 7 correct answers.