Question

Помогите пожалуйста срочно!!!!!

1. Задано точки А(0; 1; –1), В(1; –1; 2), С(3; 1; 0) , D(2; 1; 1). Знайдіть суму векторів

AD i CD =

AC i BD =

CA i DC =

DA i BC =
2. Знайдіть координати вектора ū, якщо
ū = -1/2ā і ā (4; –2; 0)

Answer 1

AD = D - A = (2; 1; 1) - (0; 1; -1) = (2; 0; 2)
CD = D - C = (2; 1; 1) - (3; 1; 0) = (-1; 0; 1)
AD + CD = (2; 0; 2) + (-1; 0; 1) = (1; 0; 3)

AC = C - A = (3; 1; 0) - (0; 1; -1) = (3; 0; 1)
BD = D - B = (2; 1; 1) - (1; -1; 2) = (1; 2; -1)
AC + BD = (3; 0; 1) + (1; 2; -1) = (4; 2; 0)

CA = A - C = (0; 1; -1) - (3; 1; 0) = (-3; 0; -1)
DC = C - D = (3; 1; 0) - (2; 1; 1) = (1; 0; -1)
CA × DC = (-3; 0; -1) × (1; 0; -1) = (-1; -2; 0)

DA = A - D = (0; 1; -1) - (2; 1; 1) = (-2; 0; -2)
BC = C - B = (3; 1; 0) - (1; -1; 2) = (2; 2; -2)
DA × BC = (-2; 0; -2) × (2; 2; -2) = (-4; 2; 4)

ū = -1/2 ā + ā = (-1/2 + 4; 1 - 2; 0) = (7/2; -1; 0)