Option 4 DHS 2.1

Option 4 DHS 2.1

DHS - 2.1
№ 1.4. 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 = -6; δ = -4; k = 3; ℓ = 2; φ = 5π / 3; λ = -1; μ = 1/2; ν = 2; τ = 3.
No. 2.4. 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 point M; dividing the segment ℓ in relation to α :.
Given: A (2; 4; 3); B (3; 1; –4); C (–1; 2; 2); .......
No. 3.4. 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; 4); b (-2; 5; 0); c (3; –2; –4); d (13; –5; –4) ..