Vectors

A vector in the plane is an object with both magnitude (length) and direction. It can be represented as an ordered pair $(x, y)$, which shows how far to move in the $x$ and $y$ directions from a starting point.

Important properties

• Vectors can be added together: $(a, b) + (c, d) = (a + c, b + d)$.

• A vector can be multiplied by a number (scalar): $k(a, b) = (ka, kb)$.

• The zero vector $(0, 0)$ has zero length and no direction.

• Two vectors are equal if they have the same length and direction, regardless of where they start.