IDZ 2.1 - Option 9. 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)
  1.9 α = -3, β = -2, γ = 1, δ = 5, k = 3, l = 6, φ = 4π / 3, λ = -1, μ = 2, ν = 1, τ = 1

  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
  2.9 A (3, 4, -4), B (-2, 1, 2), C (2, -3, 1) a = 5CB + 4AC, b = c = BA, d = AC, l = BA, 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.
  3.9 a (0, 2, 3); b (4, -3, -2); c (-5, -4, 0); d (-19, -5, -4)