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)
  1.22 α = -7, β = 2, γ = 4, δ = 6, k = 2, l = 9, φ = π / 3, λ = 1, μ = 2, ν = -1, τ = 3

  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
  2.22 A (-5, -2, -6), B (3, 4, 5), C (2, -5, 4) a = 8AC - 5BC, b = c = AB, d = BC, l = AC , 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.
  3.22 a (7, 2, 1); b (3, -5, 6); c (-4, 3, 4); d (-1, 18, -16)

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