# Option 9 2.1 Collection DHS DHS Ryabushko

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# Description

DHS - 2.1
№ 1.9. 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 = -3; β = -2; γ = 1; δ = 5; k = 3; ℓ = 6; φ = 4π / 3; λ = -1; μ = 2; ν = 1; τ = 1.
№ 2.9. From 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
M dividing points a segment ℓ against α :.
Given: A (3, 4, -4), B (-2, 1, 2); C (2, -3, 1); .......
№ 3.9. Prove that the vector a; b; c and form a basis to find the coordinates of the vector d in this basis.
Given: a (0, 2, 3); b (4, - 3, -2); c (-5; -4; 0); d (-19; -5; -4).