IDZ 2.1 - Option 4. 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)
1.4 α = 5, β = 2, γ = -6, δ = -4, k = 3, l = 2, φ = 5π / 3, λ = -1, μ = 1/2, 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
2.4 A (2, 4, 3), B (3, 1, -4), C (-1, 2, 2) a = 2BA + 4AC, b = BA, c = b, d = AC, l = BA , α = 1, 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.
3.4 a (1, 3, 4); b (-2, 5, 0); c (3, -2, -4); d (13, -5, -4)