Option 9 DHS 2.1

Option 9 DHS 2.1

DHS - 2.1
No. 1.9. 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 = -3; β = -2; γ = 1; δ = 5; k = 3; ℓ = 6; φ = 4π / 3; λ = -1; μ = 2; ν = 1; τ = 1.
No. 2.9. 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 with respect to α :.
Given: A (3; 4; –4); B (–2; 1; 2); C (2; –3; 1); .......
No. 3.9. Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a (0; 2; –3); b (4; -2; -2); c (–5; –4; 0); d (–19; –5; –4).