RAP IDZ 2.1 option 11

IDZ - 2.1
№ 1.11. The vectors are given by 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) the projection (ν · a + τ · b) on b; c) cos (a + τ · b).
Given: α = -2; β = 3; γ = 3; δ = -6; k = 6; ℓ = 3; φ = 5π / 3; λ = 3; μ = -1/3; ν = 1; τ = 2.
№ 2.11. From the coordinates of the points A; B and C for these vectors, find: a) the modulus of the vector a; b) scalar product of vectors a and b; c) the projection of the vector c onto the vector d; d) the coordinates of the point M; dividing the segment ℓ with respect to α:.
Given: A (-2; -3; -4); In (2; -4; 0); C (1; 4; 5); .......
№ 3.11. Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a (5; 3; 1); b (-1; 2; -3); c (3; -4; 2); d (-9; 34; -20).