Question

Find a vector a with representation given by the directed line segment ab. a(2, 0, −1), b(2, 2, 3)

Answer 1

The first thing you should know is that you have two points in the space:
 a (2, 0, -1)
 b (2, 2, 3)
 To form the ab vector we have:
 ab = b - a = (2, 2, 3) - (2, 0, -1)
 ab = (0, 2, 4)
 Or equivalently:
 ab = 0i + 2j + 4k
 answer:
 a vector with a representation given by the directed line segment ab is
 ab = 0i + 2j + 4k