IDZ 2.1 - Option 29. 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)
  1.29 α = 5, β = 3, γ = -4, δ = -2, k = 6, l = 3, φ = 5π / 3, λ = -2, μ = -1/2, ν = 3, τ = 2

  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
  2.29 A (3, 5, 4), B (4, 2, -3), C (-2, 4, 7) a = 3BA - 4AC, b = AB, 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.
  3.29 a (5, 7, -2); b (-3, 1, 3); c (1, -4, 6); d (14, 9, 1)