# Version 2.1 Collection of 14 DHS DHS Ryabushko

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# Description

DHS - 2.1
№ 1.14. Given a 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) projection (ν · a + τ · b) to b; a) cos (a + τ · b).
Given: α = -2; β = 3; γ = 5; δ = 1; k = 2; ℓ = 5; φ = 2π; λ = -3; μ = 4; ν = 2; τ = 3.
№ 2.14. From the coordinates of points A; B and C for the indicated vectors to find: a) the magnitude of a;
b) the scalar product of a and b; c) the projection of c-vector d; g) coordinates
Points M; dividing the interval ℓ against α :.
Given: A (10, 6, 3); B (-2, 3, 5); C (3, -4, -6); .......
№ 3.14. Prove that the vector a; b; c and form a basis to find the coordinates of the vector d in this basis.
Given: a (4; 2; 3); b (-3; 1 -8); c (2, -4, 5); d (-12; 14; -31).