RAP IDZ 2.1 option 27

DHS - 2.1
№ 1.27. 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 = -3; β = 4; γ = 5; δ = -6; k = 4; ℓ = 5; φ = π; λ = 2; μ = 3; ν = -3; τ = -1.
№ 2.27. 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 (6; 5; 4); The (-5, -2, 2) C (3, 3, 2); .......
№ 3.27. Prove that the vector a; b; c and form a basis to find the coordinates of the vector d in this basis.
Given: a (4, 5, 1); b (1; 3, 1); c (-3; - 6; 7); d (19; 33; 0)