IDZ 2.1 - Option 16. 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)
  1.16 α = -5, β = 3, γ = 2, δ = 4, k = 5, l = 4, φ = π, λ = -3, μ = 1/2, ν = -1, τ = 1

  2. The coordinates of points A, B and C for the indicated vectors to find: a) a unit vector; 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
  2.16 A (-2, 3, -4), B (3, -1, 2), C (4, 2, 4) a = 7AC + 4CB, b = c = AB, d = CB, l = AB, α = 2, β = 5

  3. Prove that the vectors a, b, c form a basis, and to find the coordinates of the vector d in this basis.
  3.16 a = (1, 3, 6); b = (-3, 4, -5); c = (1, -7, 2); d = (-2, 17, 5)