The Vector Equation of a Line (AQA A-Level Further Maths): Flashcards

Magnitude and direction

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

At point with position vector $\mathbf{a}$

Subtract one position vector from the other

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

That coordinate constant; line in a plane

Substitute coords; check same $\lambda$ all components

Not parallel and do not intersect

Parallel, intersecting, or skew

Direction vectors parallel AND share common point