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Vector Equation for a Line in R^3

Vector Equation for a Line in R^3
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2014-12-04 10:14
VectorCoordinate GeometrySolid Geometry
In collections Calc 2
This example demonstrates the vector equation of a line in R^3. Key mathematical concepts include vectors and 3D coordinate geometry. Using GeoGebra commands Line and Vector, a line is constructed, and the vector r, direction vector v, and point p are shown. Suitable for high school and above students learning the vector equation of a line in 3D space.

GeoGebra Commands & Parameters

  1. Line((1, 2, 2), Vector[(1, 2, 2), (3, -1, 3)]) → L
  2. Vector((0, 0, 0), (1 + (2 * t), 2 - (3 * t), 2 + t)) → r
  3. Vector((2, -3, 1)) → v
  4. Vector((1, 2, 2), (3, -1, 3)) → w

AI Drawing Prompt Reference

Draw a line in 3D space to demonstrate its vector equation. Include a vector starting at (1,2,2) and directed towards (3,-1,3). Also show a vector r defined by a parametric equation with origin and endpoint varying according to t, following the direction (1,-3,1). Add a fixed direction vector (2,-3,1) and a vector connecting the starting point (1,2,2) to (3,-1,3).
The prompt above was compiled from the original drawing commands and is for reference only.