Example 2: Sketching the Tangent Vector

In this video I go over another example on derivatives of vector functions, and this time sketch the tangent vector to a plane curve manually as well as with GeoGebra's 3D graphing calculator. The tangent vector is just the derivative of the vector function, and is tangent to the curve for any given value of t. Eliminating the parameter t in the parametric equations of the given vector function yields a parabolic plane curve.

#math #science #calculus #vectors #geogebra

Timestamps:

- Example 2: Sketch the Tangent Vector: 0:00
- Tangent vector and position vector at t = 1: 2:05
- Curve is a parabolic plane curve, after eliminating t from parametric equations: 3:00
- Sketching the position and tangent vector by hand: 5:20
- Tangent vector always points in the direction of increasing t: 8:47
- Graphing out the plane curve and tangent vector in GeoGebra: 9:36

Notes and playlists:

- Summary: https://inleo.io/threads/view/mes/re-leothreads-2zsw9sd8j
- Notes: https://peakd.com/hive-128780/@mes/hfsetrue
- Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FgQ3jBd9IFaWOakOWbHous
- Vector Functions playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FgQ3jBd9IFaWOakOWbHous .

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