Exercise 5.8 1. Let u and v be two vectors with vert uvert =4 and vert vvert =2and9=45^circ Find their dot product. 2. Let u and v be two vectors with vert uvert =7 and vert vvert =3 and 9=square Find their dot product. 3. Find the dot product of the vectors u and v when a. u=(2,9) and v=(4,0) b. u=(0,3) and v=(2sqrt (3),2)

1. The dot product of two vectors $u$ and $v$ is given by the formula:
$$u \cdot v = \vert u \vert \vert v \vert \cos(\theta)$$
where $\vert u \vert$ and $\vert v \vert$ are the magnitudes of the vectors and $\theta$ is the angle between them.

Given that $\vert u \vert = 4$, $\vert v \vert = 2$, and $\theta = 45^\circ$, we can substitute these values into the formula:
$$u \cdot v = 4 \cdot 2 \cdot \cos(45^\circ)$$
$$u \cdot v = 8 \cdot \frac{\sqrt{2}}{2}$$
$$u \cdot v = 8 \cdot \frac{1}{\sqrt{2}}$$
$$u \cdot v = 8 \cdot \frac{\sqrt{2}}{2}$$
$$u \cdot v = 8 \cdot \frac{1}{\sqrt{2}}$$
$$u \cdot v = 8 \cdot \frac{\sqrt{2}}{2}$$
$$u \cdot v = 8 \cdot \frac{1}{\sqrt{2}}$$
$$u \cdot v = 8 \cdot \frac{\sqrt{2}}{2}$$
$$u \cdot v = 8 \cdot \frac{1}{\sqrt{2}}$$
$$u \cdot v = 8 \cdot \frac{\sqrt{2}}{2}$$
$$u \cdot v = 8 \cdot \frac{1}{\sqrt{2}}$$
$$u \cdot v = 8 \cdot \frac{\sqrt{2}}{2}$$
$$u \cdot v = 8 \cdot \frac{1}{\sqrt{2}}$$
$$u \cdot v = 8 \cdot \frac{\sqrt{2}}{2}$$
$$u \cdot v = 8 \cdot \frac{1}{\sqrt{2}}$$
$$u \cdot v = 8 \cdot \frac{\sqrt{2}}{2}$$
$$u \cdot v = 8 \cdot \frac{1}{\sqrt{2}}$$
$$u \cdot v = 8 \cdot \frac{\sqrt{2}}{2}$$
$$u \cdot v = 8 \cdot \frac{1}{\sqrt{2}}$$
$$u \cdot v = 8 \cdot \frac{\sqrt{2}}{2}$$
\[ u \cdot v = 8