Question

Cho tam giác ABC vuông tại A có AB=3cm; AC=4cm

Tính a, \(\left|\overrightarrow{AB}-\overrightarrow{AC}\right|\)

b, \(\left|\overrightarrow{AB}+\overrightarrow{AC}\right|\)

Answer 1

Lời giải:
a)

Theo định lý Pitago:

\(BC=\sqrt{AB^2+AC^2}=\sqrt{3^2+4^2}=5\)

\(\Rightarrow |\overrightarrow{AB}-\overrightarrow{AC}|=|\overrightarrow{AC}+\overrightarrow{CB}-\overrightarrow{AC}|=|\overrightarrow{CB}|=5\)

b)

\((|\overrightarrow{AB}+\overrightarrow{AC}|)^2=AB^2+AC^2+2\overrightarrow{AB}.\overrightarrow{AC}\)

\(=AB^2+AC^2=3^2+4^2=25\)

(nhớ rằng \(AB\perp AC\Rightarrow \overrightarrow{AB}.\overrightarrow{AC}=\overrightarrow{0}\) )

\(\Rightarrow |\overrightarrow{AB}+\overrightarrow{AC}|=5\)