IDZ 2.1 - Option 28. 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)
 1.28 α = six, β = -7, γ = -1, δ = -3, k = 2, l = 6, φ = 4π / 3, λ = 3, μ = -2, ν = 1, τ = 4

 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
 2.28 A (-3, -5, 6), B (3, 5, -4), C (2, 6, 4) a = 4AC -5BA, b = CB, c = BA, d = AC, l = BA, α = 4, 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.
 3.28 a (1, -3, 1); b (-2, -4, 3); c (0, 2, 3); d (-8, -10, 13)