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)
  1.20 α = 3, β = -5, γ = -2, δ = 3, k = 1, l = 6, φ = 3π / 2, λ = 4, μ = 5, 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
  2.20 A (5, 4, 4), B (-5, 2, 3), C (4, 2, -5) a = 11AC - 6AB, b = BC, c = AB, d = AC, l = BC , α = 3, β = 1

  3. Prove that the vectors a, b, c form a basis, and to find the coordinates of the vector d in this basis.
  3.20 a (11 1 2); b (-3, 3, 4); c (-4, -2, 7); d (-5, 11, -15)

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