# Option 3 2.1 Collection DHS DHS Ryabushko

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# Description

IDZ - 2.1
No. 1.3. The vectors are given by 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 = -2; γ = -3; δ = -1; k = 4; ℓ = 5; φ = 4π / 3; λ = 2; μ = 3; ν = -1; τ = 5.
№ 2.3. From the coordinates of the points A; B and C for these vectors, find: a) the modulus of the vector a; b) scalar product of vectors a and b; c) the projection of the vector c onto the vector d; d) coordinates of points M; dividing the segment ℓ with respect to α:.
Given: A (-2; -2; 4); B (1; 3; -2); C (1; 4; 2); .......
№ 3.3. Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a (- 1; 1; 2); b (2; -3; -5); c (-6; 3; -1); d (28; -19; -7).