벡터의 크기

$\displaystyle \vec{a} \bullet \vec{b} = | \vec{a} | \bullet | \vec{b} | \cos 60 ^{\circ} = | \vec{a} | \bullet \frac{1}{2}$ $\displaystyle \vec{a} - 3 \vec{b} = \sqrt{13}$이므로 ${| \vec{a} - 3 \vec{b} |} ^{2} = 13$ $( \vec{a} - 3 \vec{b} ) ( \vec{a} - 3 \vec{b} ) = 13$ $\rightarrow \vec{a} \bullet \vec{a} - 6 \vec{a} \bullet \vec{b} + 9 \vec{b} \bullet \vec{b} = 13$ $\rightarrow | \vec{a} | - 3 | \vec{a} | + 9 = 0$ $\rightarrow | \vec{a} | - 3 | \vec{a} | - 4 = 0$ $\rightarrow ( | \vec{a} | - 4 ) ( | \vec{a} | + 1 ) = 0$ $\therefore | \vec{a} | = 4$