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

  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
  2.5 A (2, 4, 5), B (1, 2, 3), C (-1, -2, 4) a = 3AB - 4AC, b = BC, c = b, d = AB, 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.
  3.5 a (1, -1, 1); b (-5, -3, 1); c (2, 1, 0); d (-15, -10, 5)

Detailed solution. Designed in PDF format for easy viewing of IDZ solutions on smartphones and PCs. In MS Word (doc format) sent additionally.