Vector Equation of a Tangent Line on a Space Curve

In this video, I go through obtaining the vector equation of a tangent line to a space curve, by replacing the parallel vector with the tangent vector from the general vector equation of a line. This was part of Question 3 of the Concept Check review, and I have expanded the tutorial at the end to illustrate how the vectors are added together in the tangent line equation.

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#math #vectors #calculus #education #tangent

Timestamps

• Concept Check Question 3: Tangent vector, tangent line, and unit tangent vector: 0:00
• Solution: Tangent vector is derivative of position vector – 0:13
• Unit tangent vector is tangent vector divided by its magnitude, so length becomes 1 – 0:25
• Recap on vector equation of a line – 1:26
• Vector equation of the tangent line – 2:30
• Tangent line has parallel vector equal to tangent vector – 3:33
• Tangent line is the vector addition of the initial position vector and a scalar multiple of the tangent vector – 4:50

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