IDZ 2.1 - Option 2. Decisions Ryabushko AP

1. Given the vectors a = αm + βn and b = γm + δn, where | m | = k; | n | = l; (m, ^ n) = φ.
  Find a) (λa + μb) ∙ (νa + τb); b) PRV (νa + τb); a) cos (a, ^ τb)
  1.2 α = -2, β = 3, γ = 4, δ = -1, k = 1, l = 3, φ = π, λ = 3, μ = 2, ν = -2, τ = 4

2. The coordinates of points A, B and C for the indicated vectors to find: a) a unit vectors; b) the inner product of vectors a and b; c) the projection of c-vector d; z) coordinates of the point M, dividing the segment l against α: β
2.2 A (4, 3, -2), B (-3, -1, 4), C (2, 2, 1) a = -5AC + 2CB, b = AB, c = AC, d = CB, l = BC, α = 2, β = 3

3. Prove that the vectors a, b, c form a basis, and to find the coordinates of the vector d in this basis.
3.2 a (2, 1, 4); b (-3, 0, -2); c (4, 5, -3); d (0, 11, -14)