Activity 9.4.3

Determine each of the following:

1. The length of the vector $\vu=\langle 1, 2, -3 \rangle$ using the dot product.

2. The angle between the vectors $\vu =\langle 1, 2 \rangle$ and $\vv = \langle 4, -1 \rangle$ to the nearest tenth of a degree.

3. The angle between the vectors $\vy =\langle 1, 2, -3 \rangle$ and $\vz = \langle -2, 1, 1 \rangle$ to the nearest tenth of a degree.

4. If the angle between the vectors $\vu$ and $\vv$ is a right angle, what does the expression $\vu \cdot \vv = \vecmag{\vu} \vecmag{\vv} \cos(\theta)$ say about their dot product?

5. If the angle between the vectors $\vu$ and $\vv$ is acute—that is, less than $\pi/2$—what does the expression $\vu\cdot\vv=\vecmag{\vu}\vecmag{\vv}\cos(\theta)$ say about their dot product?

6. If the angle between the vectors $\vu$ and $\vv$ is obtuse—that is, greater than $\pi/2$—what does the expression $\vu\cdot\vv=\vecmag{\vu}\vecmag{\vv}\cos(\theta)$ say about their dot product?