No.1 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) the projection (ν · a + τ · b) on b; c) cos (a + τb).
Given: α = -3; β = 5; γ = 1; δ = 7; k = 4; ℓ = 6; φ = 5π/3; λ = -2; μ = 3; ν = 3; τ = -2.

No.2 According to the coordinates of points A; B and C for the indicated vectors find: a) the module of the vector a;
b) the scalar product of the vectors a and b; c) the projection of the vector c onto the vector d; d) coordinates
points M; dividing the segment ℓ with respect to α :.
Given: А(6;4; 5); В(–7; 1; 8);С(2; –2; –7); ...

No.3 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(–2; 4;1); c(4; –5; –1); d(–5; 11; 1).