Vector Planes (Edexcel A-Level Further Mathematics): Flashcards

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

Position vector of a fixed point on the plane

Non-parallel direction vectors lying on the plane

$ax + by + cz = d$

Normal vector perpendicular to the plane

$\mathbf{n} = \mathbf{b} \times \mathbf{c}$

Perpendicular to both direction vectors

$d = ax_1 + by_1 + cz_1$

Direction vectors lie in plane; normal perpendicular to plane

Find two direction vectors from the points