Cho ba vec tơ a, b, c thỏa mãn: trị tuyệt đối vecto a = 4, trị tuyệt đối vecto b = 1

* Hướng dẫn giải

Đáp án A

Ta có: $5\left(\overrightarrow{b}-\overrightarrow{a}\right)+3\overrightarrow{c}=\overrightarrow{0}$

$$\begin{gathered} \iff 5\left(\overrightarrow{a}-\overrightarrow{b}\right)=3\overrightarrow{c}\iff 25{\left(\overrightarrow{a}-\overrightarrow{b}\right)}^2=9{\overrightarrow{c}}^2 \\ \iff 25\left({\overrightarrow{a}}^2-2\overrightarrow{a}\overrightarrow{b}+{\overrightarrow{b}}^2\right)=9{\overrightarrow{c}}^2\iff \overrightarrow{a}.\overrightarrow{b}=4 \end{gathered}$$

Tương tự:

$$\begin{gathered} 5\left(\overrightarrow{b}-\overrightarrow{a}\right)+3\overrightarrow{c}=\overrightarrow{0}\iff 5\overrightarrow{a}=5\overrightarrow{b}+3\overrightarrow{c} \\ \iff \overrightarrow{b}.\overrightarrow{c}=5 \\ 5\left(\overrightarrow{b}-\overrightarrow{a}\right)+3\overrightarrow{c}=\overrightarrow{0}\iff 5\overrightarrow{b}=5\overrightarrow{a}-3\overrightarrow{c} \\ \iff \overrightarrow{a}.\overrightarrow{c}=20 \end{gathered}$$

Vậy M = 4 + 5 + 20 = 29