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IDZ 2.1 - Option 10. Decisions Ryabushko AP
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Uploaded: 15.06.2020
Content: 10v-IDZ2.1.doc 151 kB
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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)
1.10 α = 5, β = -3, γ = 4, δ = 2, k = 4, l = 1, φ = 2π / 3, λ = 2, μ = -1/2, ν = 3, τ = 0
2. The coordinates of points A, B and C for the indicated vectors to find: a) a unit vectors; 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
2.10 A (0, 2, 5), B (2, 3, 4), C (3, 2, -5) a = -3AB + 4AB, b = c = AC, d = AB, l = AC, α = 3, 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.
3.10 a (3, -1, 2); b (-2, 3, 1); c (4, -5, -3); d (-3, 2, 3)
Additional information
Detailed solution. Decorated in Microsoft Word 2003. (Target decided to use formula editor)
For the convenience of viewing IDZ solutions on smartphones, an additional file in PDF format is sent
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