Option 21 DHS 2.1

DHS - 2.1
№ 1.21. 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 = -6; γ = 2; δ = 7; k = 2; ℓ = 7; φ = π; λ = -2; μ = 5; ν = 1; τ = 3.
No. 2.21. 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 (3; 4; 6); B (–4; 6; 4); C (5; –2; –3); .......
No. 3.21. Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a (9; 5; 3); b (–3; 2; 1); c (4; –7; 4); d (–10; –13; 8)