IB Maths AI 3.10 Definitions

Describes two lines that are the same line, meaning their direction vectors are parallel and they share at least one common point.

A non-zero vector parallel to a line that gives its direction; in $r=a+\lambda b$, $b$ determines how $r$ changes as $\lambda$ changes.

Describes two lines that share a common point, found by solving their parametric equations simultaneously for a consistent set of parameter values.

A way to describe a line by writing each coordinate as a function of a parameter, for example $x=x_0+λl$, $y=y_0+λm$, $z=z_0+λn$.

A vector from the origin to a point, used to locate the point in space; in $r=a+\lambda b$, $\textbf{a}$ is the position vector of a fixed point on the line.

A real number (such as $λ$ or $μ$) that varies to generate different points on a line in a parametric or vector equation.

Describes two lines in three dimensions that are not parallel and do not meet, so no common solution exists when their parametric equations are solved together.

A representation of a line in 2D or 3D written as a position vector $\textbf{r}$ in terms of a fixed point and a scalar parameter, typically in the form $r = a + \lambda b$.