Question

Найти длину вектора BC+5*AB
A (3; -4; -3)
B (-4; 1; -5)
C (5; 3; -4)
D (4; -2; 3)

Answer 1

$\vec{BC} = \{5+4;3-1;-4+5\} =\{9;2;1\}\\ \vec{AB} = \{-4-3;1+4;-5+3\} =\{-7;5;-2\}\\ \vec{BC}+5\vec{AB} = \{9;2;1\}+5\{-7;5;-2\} = \{9-35;2+25;1-10\}=\\=\{-26;27;-9\}\\ |\vec{BC}+5\vec{AB}|=\sqrt{(-26)^2+27^2+(-9)^2}=\sqrt{676+729+81}=\\ =\sqrt{1486}$