Vector Lines (Edexcel A-Level Further Mathematics): Quizzes

$\sin \theta$

Direction vectors

Normal vectors

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

Normal vector to the plane

Neglecting to normalise vectors

Cartesian form

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

Finding angles between vectors

Using $\cos \theta$ for line-plane angle

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

Direction vectors of the lines