IDZ 2.1 - Option 15. 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)

1.15 α = 4, β = -3, γ = 5, δ = 2, k = 4, l = 7, φ = 4π / 3, λ = -3, μ = 2, ν = 2, τ = -1

• 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

• 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)

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