IDZ 2.1 - Option 12. 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)
  1.12 α = -2, β = -4, γ = 3, δ = 1, k = 3, l = 2, φ = 7π / 3, λ = -1/2, μ = 3, ν = 1, τ = 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
  2.12 A (-2, -3, -2), B (1, 4, 2), C (1, 3, 3) a = 2AC - 4BC, b = c = AB, d = AC, l = BC , α = 3, β = 1

  3. Prove that the vectors a, b, c form a basis, and to find the coordinates of the vector d in this basis.
  3.12 a (3, 1, 3); b (-2, 4, 1); c (1, 2, 5); d (1, 12, -20)