IDZ 2.1 - Option 18. 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)
  1.18 α = 7, β = -3, γ = 2, δ = 6, k = 3, l = 4, φ = 5π / 3, λ = 3, μ = -1/2, ν = 2, τ = 1

  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
  2.18 A (2, 4, 6), B (-3, 5, 1), C (4, -5, -4) a = -6BC + 2BA, b = c = CA, d = BA, l = BC , α = 1, β = 3

  3. Prove that the vectors a, b, c form a basis, and to find the coordinates of the vector d in this basis.
  3.18 a (3, 5, 4); b (-2, 7, -5); c (6, -2, 1); d (6, -9, 22)