Angle between Lines (Edexcel A-Level Further Mathematics): Flashcards

Find angles; plane equations; line/plane/plane angles

$\mathbf{a} \cdot \mathbf{b} = |\mathbf{a}| |\mathbf{b}| \cos \theta$

Direction vectors

$\cos \theta = \frac{\mathbf{b}_1 \cdot \mathbf{b}_2}{|\mathbf{b}_1||\mathbf{b}_2|}$

$\mathbf{r} \cdot \mathbf{n} = k$

Vector perpendicular to the plane

Normal vectors

$\cos \theta = \frac{\mathbf{n}_1 \cdot \mathbf{n}_2}{|\mathbf{n}_1||\mathbf{n}_2|}$

Complementary angles

$\sin \theta = \frac{\mathbf{b} \cdot \mathbf{n}}{|\mathbf{b}||\mathbf{n}|}$