IDZ 2.1 - Option 26. 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)
  1.26 α = -3, β = 5, γ = 1, δ = 7, k = 4, l = 6, φ = 5π / 3, λ = -2, μ = 3, ν = 3, 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
  2.26 A (6, 4, 5), B (-7, 1, 8), C (2, -2, -7) a = 5CB -2AC, b = AB, c = CB, d = AC, l = AB, α = 3, β = 2

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