Problem
Find the dot product, \( \vec{u} \cdot \vec{w} \). \[ \begin{array}{l} \vec{u}=\langle-7,-4\rangle \\ \vec{w}=\langle 4,-3\rangle \end{array} \] \[ \vec{u} \cdot \vec{w}=[?] \]
Solution
Step 1 ：\( \vec{u} \cdot \vec{w} = (-7)(4) + (-4)(-3) \)
Step 2 ：\( \vec{u} \cdot \vec{w} = -28 + 12 \)
Step 3 ：\( \vec{u} \cdot \vec{w} = -16 \)
