RAP IDZ 2.1 option 29

DHS - 2.1
№ 1.29. 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 = 3; γ = - 4; δ = -2; k = 6; ℓ = 3; φ = 5π / 3; λ = -2; μ = -1/2; ν = 3; τ = 2.
№ 2.29. 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; 5; 4); V (4; 2; 3); C (-2, 4, 7); .......
№ 3.29. Prove that the vector a; b; c and form a basis to find the coordinates of the vector d in this basis.
Given: a (5, 7, -2); b (-3; 1; 3); c (1, -4, 6); d (14; 9; - 1).