Definition
Vector
In geometry, a vector records a directed displacement, such as 3 right and 2 down.
What it means
A vector is a move instruction that does not care where you start. The vector (3, −2) tells every point to go 3 units right and 2 units down. Starting places differ, but the move is identical.
Remember it
Vector means the same arrow can start anywhere.
Example
Point A is (1, 4). Adding the vector (3, −2) gives A′ = (4, 2). Point B at (−2, 5) moves by the same vector to B′ = (1, 3).
Watch for
A single location is a point, not a vector; a vector describes the directed change from one location to another.
Common mix-up
The pair (3, −2) can name a point or a vector. Context tells whether it is a location or a move.
Exact meaning
In this geometry sense, a vector is a directed displacement with magnitude and direction, represented by an arrow or coordinate components. A translation by that vector moves every point by the same displacement.