Geometry
# Dot Product of Vectors

For what values of $b$ are the two vectors $(-4, b)$ and $(b, {b}^{2} )$ orthogonal?

Which of the following are correct where $\vec{a}$ and $\vec{b}$ are arbitrary vectors?

**I.** $\lvert\vec{a}\cdot\vec{b}\rvert\le\lvert\vec{a}\rvert\lvert\vec{b}\rvert$

**II.** $\lvert\vec{a}+\vec{b}\rvert\le\lvert\vec{a}\rvert+\lvert\vec{b}\rvert$

**III.** $\lvert\vec{a}-\vec{b}\rvert\le\lvert\vec{a}\rvert-\lvert\vec{b}\rvert$