Option 24 DHS 2.1

DHS - 2.1
No. 1.24. Given the 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 + τ · b).
Given: α = -5; β = -7; γ = -3; δ = 2; k = 2; ℓ = 11; φ = 3π / 2; λ = -3; μ = 4; ν = -1; τ = 2.
No. 2.24 According to the coordinates of points A; B and C for the indicated vectors to find: a) the modulus of the vector a; b) the scalar product of vectors a and b; c) the projection of the vector c on the vector d; d) coordinates of the point M; dividing the segment ℓ in relation to α :.
Given: A (4; 3; 2); B (–4; –3; 5); C (6; 4; –3); .......
No. 3.24. Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a (–2; 5; 1); b (3; 2; -1); c (4; –3; 2); d (–4; 22; - 13)