Question

Cho hình vuông ABCD cạnh a, tính độ dài:

\(\overrightarrow{k} = \overrightarrow{MA} - 2\overrightarrow{MB}+3\overrightarrow{MC}-2\overrightarrow{MD}\)

Answer 1

\(\overrightarrow{k}=\overrightarrow{MA}-2\left(\overrightarrow{MA}+\overrightarrow{AB}\right)+3\left(\overrightarrow{MA}+\overrightarrow{AC}\right)-2\left(\overrightarrow{MA}+\overrightarrow{AD}\right)\)

\(=-2\overrightarrow{AB}+3\overrightarrow{AC}-2\overrightarrow{AD}\)

\(=-2\left(\overrightarrow{AB}+\overrightarrow{AD}\right)+3\overrightarrow{AC}\)

\(=-2\overrightarrow{AC}+3\overrightarrow{AC}=\overrightarrow{AC}\)

\(\Rightarrow\left|\overrightarrow{k}\right|=\left|\overrightarrow{AC}\right|=AC=a\sqrt{2}\)