 # Version 2.1 Collection of 12 DHS DHS Ryabushko

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IDZ - 2.1
No. 1.12. 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 = -2; β = -4; γ = 3; δ = 6; k = 3; ℓ = 2; φ = 7π / 3; λ = -1/2; μ = 3; ν = 1; τ = 2.
№ 2.12. 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; -2); B (1; 4; 2); C (1; -3; 3); .......
№ 3.12. 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; -3); b (-2; 4; 1); c (1; -2; 5); d (1; 12; -20). 