IDZ 2.1 - Option 30. 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)
  1.30 α = 4, β = -3, γ = -2, δ = 6, k = 4, l = 7, φ = π / 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
  2.30 A (4, 6, 7), B (2, -4, 1), C (-3, -4, 2) a = 5AB - 2AC, b = c = BC, d = AB, l = AB, α = 3, 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.
  3.30 a (-1, 4, 3); b (3, 2, 4); c (-2, -7, 1); d (6, 20, 3)