IDZ 2.1 - Option 24. 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)
  1.24 α = -5, β = -7, γ = -3, δ = 2, k = 2, l = 11, φ = 3π / 2, λ = -3, μ = 4, ν = -1, 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
  2.24 A (4, 3, 2), B (-4, -3, 5), C (6, 4, -3) a = 8AC -5BC, b = c = BA, d = AC, l = BC, α = 2, β = 5

  3. Prove that the vectors a, b, c form a basis, and to find the coordinates of the vector d in this basis.
  3.24 a (-2, 5, 1); b (3, 2, -7); c (4, 3, 2); d (-4, 22, -13)