Question

Найти длину вектора [a,b] вектор а=2n-m Вектор b=4n+m [m}=1 [n}=2 угол [n,m]= pi / 3

Answer 1

$|m|=1,; ; |n|=2,; ; <(n,m)=frac{pi}{3}\\; [a,b]=[, 2n-m,, 4n+m, ]=8[, n,n, ]+2[, n,m, ]-4[, m,n, ]-[, m,m, ]=\\=8[, n,n, ]+2[, n,m, ]+4[, n,m, ]-[, m,m, ]\\|, [, a,b, ], |=8cdot 0+6|n||m|sinfrac{pi}{3}-0=6cdot 2cdot 1cdot frac{sqrt3}{2}=6sqrt3$