Vectors between points
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.
- A(2, −1) and B(7, 3)
- AB: top 7 − 2 = 5, bottom 3 − (−1) = 4
- 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.
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