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)
  1.13 α = 4, β = 3, γ = -1, δ = 2, k = 4, l = 5, φ = 3π / 2, λ = 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
  2.13 A (5, 6, 1), B (-2, 4, -1), C (3, 3, 3) a = 3AB - 4BC, b = c = AC, d = AB, l = BC, α = 3, β = 2

  3. Prove that the vectors a, b, c form a basis, and to find the coordinates of the vector d in this basis.
  3.13 a (6, 1, 3); b (-3, 2, 1); c (-1, -3, 4); d (15, 6, -17)

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