Question

Вычислите скалярное произведение векторов m и n, m=2a-b+c n=a-2b |a|=3 |b|=2 угол межд. a,b=60 c_|_a c_|_b все векторы

Answer 1

m;n) = (2a-b+c;a-2b) = (2a;a-2b) + (-b;a-2b) + (c;a-2b) = (2a;a) + (2a;-2b) + (-b;a) + (-b;-2b) + (c;a) + (c;-2b) = 2(a;a) - 4(a;b) - (a;b) + 2(b;b) + (a;c) - 2(b;c) = 2(a;a) - 5(a;b) + 2(b;b) + (a;c) - 2(b;c)
c_|_a => (a;c) = 0
c_|_b => (b;c) = 0
(a;a) = |a|^2; (b;b) = |b|^2
(a;b) = |a| * |b| * cos (a,b) = |a| * |b| * cos 60 = 1/2 * |a| * |b|
(m;n) = 2 * 3^2 - 5 * 1/2 * 3 * 2 + 2 * 2^2 = 18 - 15 + 8 = 11