IDZ 2.1 - Option 19. Decisions Ryabushko AP

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• 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)

1.19 α = 4, β = -5, γ = -1, δ = 3, k = 6, l = 3, φ = 2π / 3, λ = 2, μ = -5, ν = 1, τ = 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

2.19 A (-4, -2, -5), B (3, 7, 2), C (4, 6, -3) a = 9BA + 3BC, b = c = AC, d = BC, l = BA , α = 4, β = 3

• Prove that the vectors a, b, c form a basis, and to find the coordinates of the vector d in this basis.

3.19 a (5, 3, 2); b (2, -5, 1); c (-7, 4, 3); d (36, 1, 15)

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