Calculus 3, Geometry of space and vectors review (Spring 2020)

0:00 Introduction
1:20 1 - Distance between two spheres
8:27 2 - Osculating plane to a curve
19:46 3 - Angle between plane and curve
29:53 4 - Decomposing acceleration
45:20 5 - Location from velocity
50:27 6 - Arc length
59:12 7 - Cylindrical/spherical coordinates
1:13:33 8 - Projection onto a plane
1:25:40 9 - Curvature
1:32:32 10 - Area of a triangle
1:37:47 11 - Surfaces in cylindrical/spherical coordinates
1:42:53 12 - Finding a line geometrically
1:48:12 13 - Cumulative arc length
1:58:58 14 - Finding a plane geometrically

[nagisacarolin]

I just thought I would point out a small arithmetic error for number 13, I believe the final answer should be sqrt(417)

[StudentbaharATiastateedu]

Would you please explain, If arctan(u) = x+c then why u = tan(x+c)? (C is constant coming from integration, and u the substitution)