Option 17 DHS 2.1

DHS - 2.1
No. 1.17. 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 = -2; γ = 3; δ = 4; k = 2; ℓ = 5; φ = π / 2; λ = 2; μ = 3; ν = 1; τ = - 2.
No. 2.17. 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 (4; 5; 3); B (–4; 2; 3); C (5; –6; –2)
No. 3.17. 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 (5; 1; –2); c (–3; 4; 5); d (26; 11; 1)