1.3 Vectors (continued)

The Magnitude of a Vector

Work through this exercise and explain your reasoning step by step.

Let $\vu = \langle 2,3\rangle$ and $\vv = \langle -1,2\rangle$. Find $\vecmag{\vu}$, $\vecmag{\vv}$, and $\vecmag{\vu+\vv}$. Is it true that $\vecmag{\vu+\vv} = \vecmag{\vu}+\vecmag{\vv}$?

Under what conditions will $\vecmag{\vw_1+\vw_2} = \vecmag{\vw_1}+\vecmag{\vw_2}$?

With the vector $\vu = \langle 2,3\rangle$, find the lengths of $2\vu$, $3\vu$, and $-2\vu$, respectively, and use proper notation to label your results.

In general, if $t$ is any scalar, how will $\vecmag{t \vw}$ be related to $\vecmag{\vw}$?

Of the vectors $\vi$, $\vj$, and $\vi+\vj$, which are unit vectors?

Find a unit vector $\vv$ whose direction is the same as $\vu = \langle -2, 3\rangle$.

Find a unit vector $\vv$ in the opposite direction to $\vu = \langle -2, 3\rangle$.