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)
  1.25 α = 5, β = -8, γ = -2, δ = 3, k = 4, l = 3, φ = 4π / 3, 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 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
  2.25 A (-5, 4, 3), B (4, 5, 2), C (2, 7, -4) a = 3BC + 2AB, b = c = CA, d = AB, l = BC, 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.
  3.25 a (3, 1, 2); b (-4, 3, -1); c (2, 3, 4); d (14, 14, 20)

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