Version 2.1 Collection of 13 DHS DHS Ryabushko

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IDZ - 2.1
No. 1.13. 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 = 4; β = 3; γ = -1; δ = 2; k = 4; ℓ = 5; φ = 3π / 2; λ = 2; μ = - 3; ν = 1; τ = 2.
№ 2.13. 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 (5; 6; 1); B (-5; 2; 6); C (3; -3; 3); .......
No. 3.13. Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a (6; 1; -3); b (2; -4; 1); c (-1; -3; 4); d (15; 6; -17).

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