DHS - 2.1
No. 1.16. 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 = 3; γ = 2; δ = 4; k = 5; ℓ = 4; φ = π; λ = -3; μ = 1/2; ν = 1; τ = 1.
No. 2.16. The coordinates of points A; B and C for the indicated vectors to find: a) the module 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 point M; dividing the segment ℓ in relation to α :.
Given: A (–2; 3; –4); B (3; –1; 2); C (4; 2; 4); .......
No. 3.16. 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; 6); b (–3; 4; –5); c (1; –7; 2); d (–2; 17; 5).