\(\overrightarrow{BC}=\left(2;3\right),\widehat{CD}=\left(-5;-5\right),\overrightarrow{AC}=\left(3;0\right)\)
\(\overrightarrow{BC}=\left(1;-3\right),\overrightarrow{AD}=\left(-4;-8\right)\)
a .
\(\overrightarrow{AB}.\overrightarrow{CD}=2.\left(-5\right)+3.\left(-5\right)=-25\)
\(\overrightarrow{BC}.\overrightarrow{AD}=1.\left(-4\right)+\left(-3\right).\left(-8\right)=20\)
b .
\(cos\widehat{BAC}=\frac{\overrightarrow{AB}.\overrightarrow{AC}}{AB.AC}=\frac{6}{\sqrt{13}.3}=\frac{2}{\sqrt{13}}\)
\(\rightarrow\widehat{BAC}\approx56^O\)
c .
\(M\in Ox\rightarrow M\left(x;0\right)\)
\(\overrightarrow{MA}=\left(1-x;2\right),\overrightarrow{MB}=\left(3-x;5\right)\)
\(\rightarrow\overrightarrow{MA}.\overrightarrow{MB}=0\)
\(\rightarrow\left(1-x\right)\left(3-x\right)+10=0\)
\(\rightarrow x^2-4+13=0\left(VN\right)\)
