Giải thích các bước giải:
\(\begin{array}{l}
\overrightarrow {AB} = (1,3) \to AB = \sqrt {{1^2} + {3^2}} = \sqrt {10} \\
\overrightarrow {AC} = (6, - 2) \to AC = \sqrt {{6^2} + {{( - 2)}^2}} = 2\sqrt {10} \\
\overrightarrow {BC} = (5, - 5) \to BC = \sqrt {{5^2} + {{( - 5)}^2}} = 5\sqrt 2 \\
a.\overrightarrow {AB} .\overrightarrow {AC} = 1.6 + 3.( - 2) = 0\\
b.C = AB + AC + BC = \sqrt {10} + 2\sqrt {10} + 5\sqrt 2 = 3\sqrt {10} + 5\sqrt 2
\end{array}\)
d. Giả sử M(x,y)
\(\begin{array}{l}
\overrightarrow {AM} = (x + 2,y - 1)\\
2\overrightarrow {CB} = ( - 10,10)\\
3\overrightarrow {MB} = ( - 3 - 3x,12 - 3y)\\
\overrightarrow {AM} + 2\overrightarrow {CB} = 3\overrightarrow {MB} \\
\to \left\{ \begin{array}{l}
x + 2 - 10 = - 3 - 3x\\
y - 1 + 10 = 12 - 3y
\end{array} \right. \leftrightarrow \left\{ \begin{array}{l}
x = \frac{5}{4}\\
y = \frac{3}{4}
\end{array} \right. \to M(\frac{5}{4},\frac{3}{4})
\end{array}\)
