RAP IDZ 2.1 option 30

DHS - 2.1
№ 1.30. 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 = 4; β = -3; γ = -2; δ = 6; k = 4; ℓ = 7; φ = π / 3; λ = 2; μ = -1/2; ν = 3; τ = 2.
№ 2.30. 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 (4; 6; 7); In (2, -4, 1) C (- 3, -4, 2); .......
№ 3.30. 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; 4; 3); b (3, 2, 4); c (-2; -7; 1); d (6; 20; 3).