RAP IDZ 2.1 option 6

IDZ - 2.1
№ 1.6. 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 = -5; γ = -3; δ = 4; k = 2; ℓ = 4; φ = 2π / 3; λ = 3; μ = -4; ν = 2; τ = 3.
No. 2.6. 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 of the dividing segment ℓ with respect to α:.
Given: A (- 1; -2; 4); B (-1; 3; 5); C (1; 4; 2); .......
No. 3.6. Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a (3; 1; 2); b (-7; -2; -4); c (-4; 0; 3); (16, 6, 15).