Space Curves: Tracing out the Tip of a Continuous Vector Function

In this video I show that a continuous vector function in 3D forms a curve in space when tracing out the point on the tip of the vector as it moves in time. Note that a continuous vector function means that its vector functions are also continuous. I go over a simple example of a space curve, which turns out to be just a line. I rewrite the vector function as parametric equations of a line and as a vector equation of a line.

#math #vectofunctions #spacecurves #education #calculus

Timestamps

• Space Curve is a continuous 3D vector function: 0:00
• Parametric equations of a space curve: 1:36
• Graphing out a space curve: by tracing out the tip of a position vector: 3:08
• Example 3: Parametric equations of a line: 5:30
• Writing vector function as a vector equation of a line: 8:51

Notes and playlists

• Summary: @mes/re-leothreads-ykedcgxi
• Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GwdMY-E9_4LsmYmO-IxcoX
• Notes: @mes/omhbcxkw
• Vector Functions playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HQl7xTQBS_O8Te8PcpNm4U .

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