Option 28 DHS 2.1

DHS - 2.1
No. 1.28. 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 = 6; β = - 7; γ = -1; δ = -3; k = 2; ℓ = 6; φ = 4π / 3; λ = 3; μ = -2; ν = 1; τ = 4.
No. 2.28. 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 (–3; –5; 6); B (3; 5; –4); C (2; 6; 4); .......
No. 3.28. Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a (1; –3; 1); b (–2; –4; 3); c (0; –2; 3); d (–8; –10; 13).