RAP IDZ 2.1 option 2

IDZ - 2.1
No. 1.2. 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 = 4; δ = -1; k = 1; ℓ = 3; φ = π; λ = 3; μ = 2; ν = -2; τ = 4.
No. 2.2. 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) coordinates
glasses M; dividing the segment ℓ with respect to α:.
Given: A (4; 3; - 2); AT 3 ; -1; 4 ); C (2; 2; 1); .......
No. 3.2. Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a (2; -1; 4); b (-3; 0; -2); c (4; 5; -3); d (0; 11; -14).