IDZ 2.1 - Option 15. 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)
 1.15 α = 4, β = -3, γ = 5, δ = 2, k = 4, l = 7, φ = 4π / 3, λ = -3, μ = 2, ν = 2, τ = -1

 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
 2.15 A (3, 2, 4), B (-2, 1, 3), C (2, -2, -1) a = 4BC - 3AC, b = BA, c = AC, d = BC, l = AC, α = 2, 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.
 3.15 a = (-2, 1, 3); b = (3, -6, 2); c = (-5, -3, -1); d = (31 -6, 22)