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 = 4; β = -3; γ = -2; δ = 6; k = 4; ℓ = 7; φ = π/3; λ = 2; μ = -1/2; 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( 4; 6; 7 ); В( 2; –4; 1 );С (– 3 ; –4; 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(–1; 4; 3); b( 3; 2; –4 ); c( –2; –7; 1 ); d( 6; 20; –3 ).