Option 3 idz 2.1 Collection of idz ryabushko

Tasks, etc – 2.1
No. 1.3. Given vectors a = α·m + β·n; b = γ·m + δ·n; |m| = k; |n| = ℓ; (m;n) = φ;
Find: a) (λ·a + μ·b) · (V·a + τ·b); b ) the projection ( V·a + τ·b) on b; C) cos( a + τ·b).
Given: α = 5; β = -2; γ = -3; δ = -1; k = 4; ℓ = 5; φ = 4π/3; λ = 2; μ = 3; ν = -1; τ = 5.
No. 2.3. By the coordinates of points A; B and C for the specified vectors, find: a) the modulus of vector a; b) the scalar product of vectors a and b; C) the projection of vector c on vector d; d) the coordinates of the point M; dividing the segment ℓ with respect to α:.
Given: A( -2; -2; 4 ); B (1; 3; -2 ); C( 1; 4; 2 ); .......
No. 3.3. Prove that the vectors a;b;c form a basis and find the coordinates of the vector d in this basis.
Given: a(– 1; 1; 2); b( 2; -3; -5); c(-6; 3; -1); d( 28; -19; -7).