Exercise 9

Verify the equality condition in Corollary 2.6, the Cauchy-Schwarz Inequality.

• Show that if $\vec{u}$ is a negative scalar multiple of $\vec{v}$ then $\vec{u}\mathbin{\smash{\bullet}}\vec{v}$ and $\vec{v}\mathbin{\smash{\bullet}}\vec{u}$ are less than or equal to zero.

• Show that $\lvert\vec{u}\mathbin{\smash{\bullet}}\vec{v}\rvert=\lvert\vec{u}\,\rvert\,\lvert\vec{v}\,\rvert$ if and only if one vector is a scalar multiple of the other.