Exercise 2

Consider the three vectors $$\uvec = \threevec1{-2}2, \hspace{24pt} \vvec = \threevec111, \hspace{24pt} \wvec = \threevec02{-1}.$$

1. Find the dot products $\uvec\cdot\uvec$, $\uvec\cdot\vvec$, and $\uvec\cdot\wvec$.

2. Use the dot products you just found to evaluate:

   1. $\len{\uvec}$.

   2. $(-5\uvec)\cdot\vvec$.

   3. $\uvec\cdot(-3\vvec+2\wvec)$.

   4. $\len{\frac1{\len{\uvec}} \uvec}$.

3. For what value of $k$ is $\uvec$ orthogonal to $k\vvec+5\wvec$?