# Option 4 2.1 Collection DHS DHS Ryabushko

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IDZ - 2.1
№ 1.4. 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 = 2; γ = -6; δ = -4; k = 3; ℓ = 2; φ = 5π / 3; λ = -1; μ = 1/2; ν = 2; τ = 3.
№ 2.4. 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; 4; 3); In (3; 1; -4); C (-1; 2; 2); .......
№ 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).