A(1; 1; 5); b(2; -4; 6); c(-5; 3; 1)
1) Скалярное произведение векторов.
2a - 2c = (2; 2; 10) - (-10; 6; 2) = (2+10; 2-6; 10-2) = (12; -4; 8)
b + 3a = (2; -4; 6) + (3; 3; 15) = (2+3; -4+3; 6+15) = (5; -1; 21)
(2a - 2c)(b + 3a) = x1*x2 + y1*y2 + z1*z2 = 12*5 + (-4)(-1) + 8*21 = 232
2) Векторное произведение векторов
2a + c = (2; 2; 10) + (-5; 3; 1) = (2-5; 2+3; 10+1) = (-3; 5; 11)
2b - 3a = (4; -8; 12) - (3; 3; 15) = (4-3; -8-3; 12-15) = (1; -11; -3)
(-3; 5; 11)x(1; -11; -3) = (y1*z2-z1*y2; z1*x2-x1*z2; x1*y2-y1*x2) =
= (5(-3)-11(-11); 11*1-(-3)(-3); (-3)(-11)-5*1) = (-15+121; 11-9; 33-5) =
= (106; 2; 28)