IDZ 2.1 - Option 10. 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)
  1.10 α = 5, β = -3, γ = 4, δ = 2, k = 4, l = 1, φ = 2π / 3, λ = 2, μ = -1/2, ν = 3, τ = 0

  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
  2.10 A (0, 2, 5), B (2, 3, 4), C (3, 2, -5) a = -3AB + 4AB, b = c = AC, d = AB, l = AC, α = 3, β = 2

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