Version 2.1 Collection of 24 DHS DHS Ryabushko

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Uploaded: 01.06.2012
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DHS - 2.1
№ 1.24. Given a 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) projection (ν · a + τ · b) to b; a) cos (a + τ · b).
Given: α = -5; β = -7; γ = -3; δ = 2; k = 2; ℓ = 11; φ = 3π / 2; λ = -3; μ = 4; ν = -1; τ = 2.
№ 2.24 The coordinates of points A; B and C for the indicated vectors to find: a) the magnitude of a;
b) the scalar product of a and b; c) the projection of c-vector d; g) coordinates
Points M; dividing the interval ℓ against α :.
Given: A (4; 3; 2); The (-4, -3, 5) C (6, 4, 3); .......
№ 3.24. Prove that the vector a; b; c and form a basis to find the coordinates of the vector d in this basis.
Given: a (-2; 5: 1); b (3; 2; - 1); c (4; -3; 2); d (-4; 22 - 13)

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