Equations of Lines in 3D (Edexcel A-Level Further Mathematics): Flashcards

$\mathbf{r} = \mathbf{a} + \lambda \mathbf{b}$

$\frac{x-a_1}{b_1} = \frac{y-a_2}{b_2} = \frac{z-a_3}{b_3}$

Position vector of any point on the line

Position vector of a fixed point on the line

Direction vector of the line

Scalar parameter

They are equivalent and represent the same line

Eliminate $\lambda$ from the parametric equations

$\mathbf{a}$ is a fixed point on the line, $\mathbf{b}$ is direction vector

Not substituting solutions back to check consistency