Complex sentence: The magnitude of the vector\\ mathbf_1 -\\ mathbf_0 is like our distance PQ above, so we desire the vector projection of this in the direction of\\ mathbf.
Split into simpler sentences: The magnitude of the vector\\ mathbf_1 -\\ mathbf_0 is like our distance PQ above. We desire the projection of this vector in the direction of\\ mathbf.