IDZ 2.1 - Option 8. 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)
  1.8 α = 5, β = 2, γ = 1, δ = -4, k = 3, l = 2, φ = π, λ = 1, μ = -2, ν = 3, 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
  2.8 A (2, -4, 3), B (-3, -2, 4), C (0, 0, -2) a = 3AC - 4CB, b = c = AB, d = CB, l = AC , α = 2, β = 1

  3. Prove that the vectors a, b, c form a basis, and to find the coordinates of the vector d in this basis.
  3.8 a (5, 1, 2); b (-2, 1, -3); c (4, 3, 5); d (15 -15, 24)