# Projection Defines a Line A line $l$ can be mathematically defined via [Projection](Projection.md) onto a fixed vector $v \in \mathbb{R}^n$. We can write $l$ as: $l = \{\boldsymbol{x} \in \mathbb{R}^n \mid \text{proj}_v(\boldsymbol{x}) = t \cdot v\}$ This can be seen visually below. All orange vectors represent our set that is projected onto the same magnitude in the direction of $v$.  This is a nice example of how we can define / construct a mathematical object, $l$, [Via Sets and Constraints](Define%20Mathematical%20Objects%20Via%20Sets%20and%20Constraints.md). --- Date: 20241025 Links to: Tags: References: * []()