Combinations of Lines & Planes (Edexcel A-Level Further Mathematics): Flashcards

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

A point on the line

Direction vector of the line

Normal vector to the plane

Substitute line eqn into plane eqn

Substitute $\lambda$ back into line eqn

$ax + by + cz + d = 0$

$\frac{|ax_1 + by_1 + cz_1 + d|}{\sqrt{a^2 + b^2 + c^2}}$

$|ax_1 + by_1 + cz_1 + d|$

$\sqrt{a^2 + b^2 + c^2}$