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

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( 2; 4; 3 ); В( 3; 1; –4 );C( –1; 2; 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; 3; 4); b(– 2; 5; 0 ); c( 3; –2; –4 ); d(13; –5 ; –4 ).