RAP IDZ 2.1 option 19

DHS - 2.1
№ 1.19. Given a vector a = α · m + β · n; b = γ · m + δ · n; | M | = k; | N | = ℓ; (M; n) = φ;
Find: a) (λ · a + μ · b) · (ν · a + τ · b); b) projection (ν · a + τ · b) to b; a) cos (a + τ · b).
Given: α = 4; β = -5; γ = -1; δ = 3; k = 6; ℓ = 3; φ = 2π / 3; λ = 2; μ = -5; ν = 1; τ = 2.
№ 2.19. From the coordinates of points A; B and C for the indicated vectors to find: a) the magnitude of a;
b) the scalar product of a and b; c) the projection of c-vector d; g) coordinates
Points M; dividing the interval ℓ against α :.
Given: A (-4, -2, -5); B (3, 7, 2); C (4; 6; -3)
№ 3.19. Prove that the vector a; b; c and form a basis to find the coordinates of the vector d in this basis.
Given: a (5, 3, 2); b (2, -5, 1); c (-7; 4; 3); d (36; 1; 15)