IDZ 2.1 - Option 17. Decisions Ryabushko AP

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)
  1.17 α = 5, β = -2, γ = 3, δ = 4, k = 2, l = 5, φ = π / 2, 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
  2.17 A (4, 5, 3), B (-4, 2, 3), C (5, -6, -2) a = 9AB - 4BC, b = c = AC, d = AB, l = BC, α = 5, 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.
  3.17 a (7, 2, 1); b (5, 1, -2); c (-3, 4, 5); d (26, 11, 1)