7.
Gọi H là trung điểm BC.
\(\left|\vec{AB}+\vec{AC}\right|=\left|2\vec{AH}\right|=2AH=\dfrac{a\sqrt{3}}{2}\)
\(\left|\vec{AB}-\vec{AC}\right|=\left|\vec{CB}\right|=BC=a\)
8.
\(\left|\vec{AB}+\vec{AC}+\vec{AD}\right|\)
\(=\left|\vec{DC}+\vec{AD}+\vec{AC}\right|\)
\(=\left|\vec{AC}+\vec{AC}\right|\)
\(=\left|2\vec{AC}\right|=2AC=2\sqrt{2}a\)
9.
\(\left|\vec{AB}+\vec{AD}\right|=\left|2\vec{AO}\right|=\left|\vec{AC}\right|=AC=\sqrt{2}a\)
Gọi M là trung điểm BC.
\(\left|\vec{AB}+\vec{AC}\right|=\left|2\vec{AM}\right|=2AM=\sqrt{a^2+\dfrac{a^2}{4}}=\dfrac{a\sqrt{5}}{2}\)
\(\left|\vec{AB}-\vec{AD}\right|=\left|\vec{DB}\right|=DB=\sqrt{2}a\)
