From A to B

The vector AB takes you from A to B, so subtract: AB = B − A, row by row. BA goes the other way, so BA = −AB.

  1. A(2, −1) and B(7, 3)
  2. AB: top 7 − 2 = 5, bottom 3 − (−1) = 4
  3. BA: top −5, bottom −4

Routes and parallel vectors

To get from A to C, you can go A to B and then B to C: AC = AB + BC. Going backwards along a vector changes its sign.

Two vectors are parallel when one is a multiple of the other: (2, 3) and (6, 9) are parallel, because (6, 9) = 3 × (2, 3). A negative multiple is parallel too, but points the other way.

First question