Option 2 DHS 2.1

DHS - 2.1
No. 1.2. 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 = -2; β = 3; γ = 4; δ = -1; k = 1; ℓ = 3; φ = π; λ = 3; μ = 2; ν = -2; τ = 4.
№ 2.2. 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; 3; - 2); IN 3 ; -one; four ); C (2; 2; 1); .......
No. 3.2. Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a (2; –1; 4); b (–3; 0; –2); c (4; 5; –3); d (0; 11; –14).