回覆 1# 小呆 的帖子
令 \(\vec{u} = 3\vec{a}+\vec{b}\) 且 \(\vec{v} = -\vec{a}+2\vec{b}\)，則
\(\displaystyle\vec{a} = \frac{2\vec{u}-\vec{v}}{7}\) 且 \(\displaystyle\vec{b} = \frac{\vec{u}+3\vec{v}}{7}\)
\(\displaystyle\Rightarrow \vec{a}\cdot\vec{b} = \frac{\left(2\vec{u}-\vec{v}\right)\cdot\left(\vec{u}+3\vec{v}\right)}{49}\)
\( \displaystyle =\frac{2\left|\vec{u}\right|^2+5\vec{u} \cdot \vec{v} -3 \left|\vec{v}\right|^2}{49}\)
\( \displaystyle \leq\frac{8+5\times 2 -3}{49}\)
\( \displaystyle =\frac{15}{49}.\)
