# Version 2.1 Collection of 16 DHS DHS Ryabushko

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IDZ - 2.1
№ 1.16. The vectors are given by 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.
№ 2.16. From the coordinates of the points A; B and C for these vectors, find: a) the modulus of the vector a; b) scalar product of vectors a and b; c) the projection of the vector c onto the vector d; d) the coordinates of the point M; dividing the segment ℓ with respect to α:.
Given: A (-2; 3; -4); In (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).  