IDZ 2.1 - Option 27. 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)
  1.27 α = -3, β = 4, γ = 5, δ = -6, k = 4, l = 5, φ = π, λ = 2, μ = 3, ν = -3, 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
  2.27 A (6, 5, -4), B (-5, -2, 2), C (3, 3, 2) a = 6AB -3CB, b = c = AC, d = CB, l = BC, α = 1, 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.
  3.27 a (4, 5, 1); b (1, 3, 1); c (-3, -6, 7); d (19, 33, 0)