Example 5: Vector and Parametric Equations of a Line Segment

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In this video I go over an example in obtaining the vector and parametric equations of a line segment between two given points. I first recap on the vector equation of a line segment, which involves a parameter t between 0 and 1. The line segment equation is essentially the position vector of the first given point subtracted by (t multiplied by that first position vector) and added by (t multiplied the position vector of the second given point). As t goes from 0 to 1, the line segment equation goes linearly from equaling the first position vector at t = 0 to equaling the second position vector at t = 1. From the vector equation, we can obtain the parametric equations of the line segment. I graph this line segment out manually as well as with the GeoGebra 3D graphing calculator: https://www.geogebra.org/calculator/uh9jnevt

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Timestamps

• Example 5: Line Segment between 2 points: 0:00

• Recap on Equation of a Line Segment: 0:45

• Vector equation of our line segment: 2:54

• Corresponding parametric equations for our line segment: 6:56

• Graphing out our line segment: 7:36

• Graphing in GeoGebra 3D graphing calculator: 10:06