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Geometry Basics.pdf

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Summary

points and vectors defined by coordinates, operations include addition, subtraction, scalar multiplication, scalar product, and vector product.
Scalar product: ⃗v1 · ⃗v2 = x1x2 + y1y2, vector product: ⃗v1 × ⃗v2 = x1y2 − x2y1.
Line equation: Ax + By = C, signed distance from point to line: (Ax0 + By0 - C) / √(A2 + B2).
Intersection of lines: Cramer's rule, baricentric line division rule.
Angle between vectors: atan2([⃗u,⃗v], (⃗u,⃗v)), rotation of vector: ⃗vφ = (x cos φ - y sin φ, x sin φ + y cos φ).
3d geometry: scalar product, vector product, mixed product, volume of parallelepiped.
Vector product: [⃗v1, ⃗v2] = (y1z2 - y2z1, z1x2 - z2x1, x1y2 - x2y1), mixed product: (⃗v1, ⃗v2, ⃗v3) = (⃗v1, [⃗v2, ⃗v3]).
Plane equation: Ax + By + Cz = D, intersection of line and plane: baricentric rule.
Distance between lines: x = (⃗AB, ⃗n), where ⃗n = [⃗u,⃗v]/|[⃗u,⃗v]|.
Spherical geometry: spherical coordinates, distance on sphere: d(⃗u,⃗v) = ̸(⃗u,⃗v) = atan2(|[⃗u,⃗v]|, ⃗u · ⃗v), arc intersection: ⃗X = [⃗n1, ⃗n2]/|⃗n1, ⃗n2|.

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points and vectors defined by coordinates, operations include addition, subtraction, scalar multiplication, scalar product, and vector product.

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File Format: PDF
File Size: 147 KB
Pages: 4
Language: EN
Total Downloads: 336
Last Updated: 5 days ago

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This PDF document about Geometry Basics provides comprehensive information and guidance. Whether you're a beginner or advanced user, this resource offers valuable insights into Geometry Basics.

Geometry Basics.pdf

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