Question

РЕБЯТА ПОМОГИТЕ ПОЖАЛУЙСТА УМОЛЯЮ) ​

Answer 1

AB(-2-1; 4 - 3; -1-2) = (-3; 1; -3), CB(-2-1; 4-3; -1+2) = (-3; 1; 1)

а = 2AB + 5CB = 2(-3; 1; -3) + 5(-3; 1; 1) = (-6; 2; -6) + (-15; 5; 5) = (-21; 7; -1)

b = AC = (0; 0; -4)

c = b = (0; 0; -4)

d = AB = (-3; 1; -3)

a) |a| = √(21² + 7² + 1²) = √(441 + 49 + 1) = √491

б) а·b = (-21; 7; -1)·(0; 0; -4) = -21·0 + 7·0 + (-1)·(-4) = 0 + 0 + 4 = 4

в) |c|·cos(∠(c,d)) = (c·d)/|d| = (0 + 0 + 12)/√(9 + 1 + 9) = 12/√19

г) A(1;3 ; 2); B(-2; 4; -1); α:β = 2:4 = 1:2

x₀ = (2x₁ + x₂)/(2 + 1) = (2·1 - 2)/3 = 0

y₀ = (2y₁ + y₂)/(2 + 1) = (2·3 + 4)/3 = 10/3

z₀ = (2z₁ + z₂)/(2 + 1) = (2·2 - 1)/3 = 3/3 = 1

M(0; 10/3; 1)