Exercise 20

Let $\vu = \langle 2, 1 \rangle$ and $\vv = \langle 1, 2 \rangle$.

1. Determine the components and draw geometric representations of the vectors $2\vu$, $\frac{1}{2}\vu$, $(-1)\vu$, and $(-3)\vu$ on the same set of axes.

2. Determine the components and draw geometric representations of the vectors $\vu + \vv$, $\vu + 2\vv$, and $\vu + 3\vv$ on the same set of axes.

3. Determine the components and draw geometric representations of the vectors $\vu - \vv$, $\vu - 2\vv$, and $\vu - 3\vv$ on the same set of axes.

4. Recall that $\vu - \vv = \vu + (-1)\vv$. Sketch the vectors $\vu$, $\vv$, $\vu+\vv$, and $\vu-\vv$ on the same set of axes. Use the “tip to tail” perspective for vector addition to explain the geometric relationship between $\vu$, $\vv$, and $\vu - \vv$.