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 = -2; γ = 3; δ = 4; k = 2; ℓ = 5; φ = π/2; λ = 2; μ = 3; ν = 1; 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(4;5; 3); В(–4;2;3); С(5; –6; –2 ); ...

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(7;2;1); b(5;1;–2); c(–3;4;5); d( 26; 11; 1 ).