Unit Vectors

Circle A has radius one, with points B and C on the circle. So vectors u and v (formed by connecting point A to points B and C respectively) will always be unit vectors. Notice u and v are a specific angle α apart - move the slider to change the angle. Vector w is the sum of vectors u and v. Move points A and B and angle α to see the relationship of u, v, and w.

For what angle(s) α is u + v also a unit vector? Can you prove this using vectors? Can you prove this using Geometry?

This applet comes from problem #9 on the Linear Algebra Review.

Jillian Maher, July 17, 2008, Created with GeoGebra