IDZ 2.1 - Option 11. 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)
 1.11 α = -2, β = 3, γ = 3, δ = -6, k = 6, l = 3, φ = 5π / 3, λ = 3, 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 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
 2.11 A (-2, -3, -4), B (2, -4, 0), C (1, 4, 5) a = 4AC - 8BC, b = c = AB, d = BC, l = AB , 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.
 3.11 a (5, 3, 1); b (-1, 2, -3); c (3, -4, 2); d (-9, 34, -20)