Consider the three points a = (10, −3,5), b = (0,2,4), and c = (2,1,0) in three-dimensional space.
let be the midpoint of and be the midpoint of .
a. write down the components of the three vectors ab, bc, and ca, and verify through arithmetic that
their sum is zero. also, explain why geometrically we expect this to be the case.
b. write down the components of the vector mn. show that it is parallel to the vector bc and half its
magnitude.