Projection Vector Proof

The video tutorial explains how to derive the formula for the projection vector of one vector onto another. It begins by introducing two generic vectors, a and b, and poses the question of how much of vector a is in the direction of vector b. The tutorial constructs a right-angle triangle to find the projection vector, named u, and explains the process of determining its magnitude and direction. The magnitude is derived using the cosine of the angle between the vectors, while the direction is determined by the unit vector of b. The final formula for the projection vector is presented, and the video concludes by discussing the symmetry in projection vectors.

What is the significance of the unit vector in finding the projection?

Describe the final formula for the projection of vector a onto vector b.

How can you derive the projection of vector b onto vector a?