IDZ 2.1 - Option 6. 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)
  1.6 α = 2, β = -5, γ = -3, δ = 4, k = 2, l = 4, φ = 2π / 3, λ = 3, μ = -4, ν = 2, τ = 3

  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
  2.6 A (-1, -2, 4), B (-1, 3, 5), C (1, 4, 2) a = 3AC -7BC, b = AB, c = b, d = AC, l = AC, α = 1, β = 7

  3. Prove that the vectors a, b, c form a basis, and to find the coordinates of the vector d in this basis.
  3.6 a (3, 1, 2); b (-7, -2, -4); c (-4, 0, 3); d (16, 6, 15)