Option 26 DHS 2.1

DHS - 2.1
No. 1.26. 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 = -3; β = 5; γ = 1; δ = 7; k = 4; ℓ = 6; φ = 5π / 3; λ = -2; μ = 3; ν = 3; τ = -2.
No. 2.26. 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 (6; 4; 5); B (–7; 1; 8); C (2; –2; –7); .......
No. 3.26. Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a (3; –1; 2); b (–2; 4; 1); c (4; –5; –1); d (–5; 11; 1).