IDZ 2.1 - Option 7. 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)
  1.7 α = 3, β = 2, γ = -4, δ = -2, k = 2, l = 5, φ = 4π / 3, λ = 1, μ = -3, ν = 0, τ = -1 / 2

  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
  2.7 A (1, 3, 2), B (-2, 4, -1), C (1, 3, -2) a = 2AB + 5CB, b = AC, c = b, d = AB, l = AB, α = 2, β = 4

  3. Prove that the vectors a, b, c form a basis, and to find the coordinates of the vector d in this basis.
  3.7 a (-3, 0, 1); b (2, 7, 3); c (-4, 3, 5); d (-16, 33, 13)