Option 29 DHS 2.1 Collection of DHS Ryabushko

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DHS - 2.1
No. 1.29. Given the 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) the projection (ν · a + τ · b) on b; c) cos (a + τ · b).
Given: α = 5; β = 3; γ = - 4; δ = –2; k = 6; ℓ = 3; φ = 5π / 3; λ = –2; μ = –1/2; ν = 3; τ = 2.
No. 2.29. The coordinates of points A; B and C for the indicated vectors to find: a) the modulus of the vector a; b) the scalar product of vectors a and b; c) the projection of the vector c on the vector d; d) coordinates of the point M; dividing the segment ℓ in relation to α :.
Given: A (3; 5; 4); B (4; 2; –3); C (–2; 4; 7); .......
No. 3.29. Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a (5; 7; –2); b (–3; 1; 3); c (1; –4; 6); d (14; 9; - 1).

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