[m]\vec{AB}=(3-(-2);-1-3;2-(-4))=(5;-4;6)[/m]
[m]\vec{CB}=(3-4;-1-2;2-4)=(-1;-3;-2)[/m]
[m]\vec{a}=7\vec{AC}+4\vec{CB}=(7*6;7*(-1);7*8)+(4*(-1);4*(-3);4*(-2))=(42+(-4);-7+(-12);56+(-8)=(38;-19;48)[/m]
a)
[m]|\vec{a}|=\sqrt{38^2+(-19)^2+48^2}=...[/m]
б)
[m]\vec{a}\cdot \vec{b}=38\cdot 5+(-19)\cdot (-4)+48\cdot 6=...[/m]
в)
пр[m]_{\vec{b}}\vec{d}=\frac{\vec{d}\cdot \vec{b}}{|\vec{b}|}=\frac{-1\cdot 5+(-3)\cdot(-4)+(-2)\cdot 6}{\sqrt{5^2+(-4)^2+6^2}}=-\frac{1}{\sqrt{3}}[/m]
г)
M(x_(M);y_(M);z_(M))
x_(M)=(2+([red]2/5[/red])*3)/(1+([red]2/5[/red]))=
y_(M)=(3+([red]2/5[/red])*(-1))/(1+([red]2/5[/red]))=
z_(M)=(-4+([red]2/5[/red])*2)/(1+([red]2/5[/red]))=