RAP IDZ 2.1 option 23

DHS - 2.1
№ 1.23. 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 = 4; γ = -6; δ = 2; k = 2; ℓ = 9; φ = 2π / 3; λ = 3; μ = 2; ν = 1; τ = -1/2.
№ 2.23. 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 (3; 4; 1); B (5; -2, 6) C (4, 2, -7); .......
№ 3.23. 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; 2; 3); b (-5; 3; -1); c (-6; 4; 5); d (-4; 11; 20)