Option 22 DHS 2.1

DHS - 2.1
No. 1.22. 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 = -7; β = 2; γ = 4; δ = 6; k = 2; ℓ = 9; φ = π / 3; λ = 1; μ = 2; ν = -1; τ = 3.
No. 2.22. 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
points M; dividing the segment ℓ in relation to α :.
Given: A (–5; –2; - 6); B (3; 4; 5); C (2; - 5; 4); .......
No. 3.22. Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a (7; 2; 1); b (3; –5; 6); c (–4; 3; –4); d (–1; 18; - 16)