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Quantum Engineering Year 0: Mathematical Foundations Month 2Day 32

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Year 0·Month 2·Week 1

Day 32: Lines and Planes in Space

Day 32 of 2,016~10 min read

Learning Objectives

•Write parametric and symmetric equations of lines
•Find equations of planes from points and normal vectors
•Determine if lines are parallel, intersecting, or skew
•Calculate distances between points, lines, and planes
•Find angles between planes

Today's Schedule (7 hours)

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Schedule Overview Learning Objectives Required Reading Primary Text Stewarts Calculus 8th Edition Video Resources MIT OpenCourseWare 1802SC Professor Leonard Part I Lines in Three Dimensions 1 Vector Equation of a Line 2 Parametric Equations 3 Symmetric Equations 4 Line Through Two Points Line Examples Example 1 Line from Point and Direction Example 2 Line Through Two Points Example 3 Parallel Intersecting or Skew Part II Planes in Three Dimensions 5 Normal Vector 6 Vector Equation of a Plane 7 Scalar Equation of a Plane 8 Finding Normal Vectors Plane Examples Example 4 Plane from Point and Normal Example 5 Plane Through Three Points Example 6 Angle Between Planes Distances Distance from Point to Plane Distance from Point to Line Example 7 Point-to-Plane Distance Example 8 Point-to-Line Distance Practice Problems Level 1 Lines Level 2 Planes Level 3 Angles and Relationships Level 4 Distances Level 5 Applications Answers Quantum Mechanics Connection Configuration Space Planes in Hilbert Space Daily Checklist Reflection Questions Preview Tomorrow

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