RAP IDZ 2.1 option 21

DHS - 2.1
№ 1.21. 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 = -5; β = -6; γ = 2; δ = 7; k = 2; ℓ = 7; φ = π; λ = -2; μ = 5; ν = 1; τ = 3.
№ 2.21. 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 (3; 4; 6); The (-4, 6, 4); C (5; -2, -3); .......
№ 3.21. Prove that the vector a; b; c and form a basis to find the coordinates of the vector d in this basis.
Given: a (9, 5, 3); b (-3; 2; 1); c (4, -7, 4); d (-10; -13; 8)