IDZ - 2.1
No. 1.7. 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 = 3; β = 2; γ = -4; δ = -2; k = 2; ℓ = 5; φ = 4π / 3; λ = 1; μ = -3; ν = 0; τ = -1/2.
No. 2.7. 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) the coordinates of the point M of the dividing segment ℓ with respect to α:.
Given: A (1; 3; 2); In (-2; 4; -1); C (1; 3; -2); .......
No. 3.7. Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a (-3; 0; 1); b (2; 7; -3); c (-4,3,5); d (-16; 33; 13).

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