Question

cho tam giác ABC vuông tại A, AB=a, AC=b.

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

Answer 1

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

Đặt \(x=\left|\overrightarrow{AB}-\overrightarrow{AC}\right|\Rightarrow x^2=AB^2+AC^2-2\overrightarrow{AB}.\overrightarrow{AC}=AB^2+AC^2=a^2+b^2\)

\(\Rightarrow x=\sqrt{a^2+b^2}\)

\(y=\left|\overrightarrow{AB}+\overrightarrow{AC}\right|\Rightarrow y^2=AB^2+AC^2+2\overrightarrow{AB}.\overrightarrow{AC}=AB^2+AC^2=a^2+b^2\)

\(\Rightarrow y=\sqrt{a^2+b^2}\)