# Option 4 2.1 Collection DHS DHS Ryabushko

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# Description

DHS - 2.1
№ 1.4. 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 = 2; γ = -6; δ = -4; k = 3; ℓ = 2; φ = 5π / 3; λ = -1; μ = 1/2; ν = 2; τ = 3.
№ 2.4. 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
Points M; dividing the interval ℓ against α :.
Given: A (2; 4; 3); In (3; 1; -4); C (-1; 2, 2); .......
№ 3.4. Prove that the vector a; b; c and form a basis to find the coordinates of the vector d in this basis.
Given: a (1; 3; 4); b (- 2, 5, 0); c (3, -2, -4); d (13, -5, -4) ..