IDZ 2.1 - Option 1. 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) etc. (νa + τb); a) cos (a, τb)
1.1 α = -5, β = -4, γ = 3, δ = 6, k = 3, l = 5, φ = 5π / 3, λ = -2, μ = 1/3, ν = 1, τ = 2

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
  2.1 A (4, 6, 3), B (-5, 2, 6), C (4, -4, -3) a = 4CB-AC, b = AB, c = CB, d = AC, l = AB, α = 5, 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.
  3.1 a (5, 4, 1); b (-3, 5, 2); c (2, 1, 3); d (7, 23, 4)