Version 2.1 Collection of 25 DHS DHS Ryabushko

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DHS - 2.1
№ 1.25. 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 = -8; γ = -2; δ = 3; k = 4; ℓ = 3; φ = 4π / 3; λ = 2; μ = -3; ν = 1; τ = 2.
№ 2.25. 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 (-5, 4, 3); In (4, 5, 2); C (2; 7; - 4); .......
№ 3.25. Prove that the vector a; b; c and form a basis to find the coordinates of the vector d in this basis.
Given: a (3, 1, 2); b (-4; 3; 1); c (2; 3; 4); d (14; 14; 20)