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)
  1.23 α = 5, β = 4, γ = -6, δ = 2, k = 2, l = 9, φ = 2π / 3, λ = 3, μ = 2, ν = 1, τ = -1/2

  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
  2.23 A (3, 4, 1), B (5, 2, 6), C (4, 2, -7) a = -7AC + 5AB, b = c = BC, d = AC, l = AB, α = 2, 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.
  3.23 a (1, 2, 3); b (-5, 3, -1); c (-6,

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