RAP IDZ 2.1 option 20

DHS - 2.1
№ 1.20. 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 = -5; γ = -2; δ = 3; k = 1; ℓ = 6; φ = 3π / 2; λ = 4; μ = 5; ν = 1; τ = -2.
№ 2.20. 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, 4); The (-5, 2, 3) C (4; 2; - 5); .......
№ 3.20. Prove that the vector a; b; c and form a basis to find the coordinates of the vector d in this basis.
Given: a (11, 1, 2); b (-3; 3; 4); c (-4; -2; 7); d (-5; 11; -15)