IDZ 2.1 - Option 17. 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)

1.17 α = 5, β = -2, γ = 3, δ = 4, k = 2, l = 5, φ = π / 2, λ = 2, μ = 3, 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

2.17 A (4, 5, 3), B (-4, 2, 3), C (5, -6, -2) a = 9AB - 4BC, b = c = AC, d = AB, l = BC, α = 5, β = 1

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

3.17 a (7, 2, 1); b (5, 1, -2); c (-3, 4, 5); d (26, 11, 1)

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