IDZ 2.1 - Option 3. 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)
1.3 α = 5, β = -2, γ = -3, δ = -1, k = 4, l = 5, φ = 4π / 3, λ = 2, μ = 3, ν = -1, τ = 5

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
2.3 A (-2, -2, 4), B (1, 3, -2), C (1, 4, 2) a = 2AC - 3BA, b = BC, c = BC, d = AC, l = BA, α = 2, 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.
3.3 a (-1, 1, 2); b (2, -3, -5); c (-6, 3, -1); d (28, -19, -7)