Exercise 4

Suppose that $\vvec=3\wvec$.

1. What is the relationship between $\vvec\cdot\vvec$ and $\wvec\cdot\wvec$?

2. What is the relationship between $\len{\vvec}$ and $\len{\wvec}$?

3. If $\vvec=s\wvec$ for some scalar $s$, what is the relationship between $\vvec\cdot\vvec$ and $\wvec\cdot\wvec$? What is the relationship between $\len{\vvec}$ and $\len{\wvec}$?

4. Suppose that $\vvec=\threevec{3}{-2}2$. Find a scalar $s$ so that $s\vvec$ has length 1.