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 =5; β = 4; γ = -6; δ = 2; k = 2; ℓ = 9; φ = 2π/3; λ = 3; μ = 2; ν = 1; τ = -1/2.

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(3;4; 1); В(5;–2; 6);С( 4;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( 1;2;3); b(–5; 3; –1);c( –6; 4;5); d( –4; 11;20 ).