Problem Solving using 3D Vectors (AQA A-Level Mathematics): Flashcards

$|\mathbf{v}| = \sqrt{v_x^2 + v_y^2 + v_z^2}$

$a_x b_x + a_y b_y + a_z b_z$

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

$\frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}| |\mathbf{b}|}$

Perpendicular to both $\mathbf{a}$ and $\mathbf{b}$

Area of parallelogram formed by $\mathbf{a}$ and $\mathbf{b}$

$\begin{pmatrix} a_x + b_x \\ a_y + b_y \\ a_z + b_z \end{pmatrix}$

$\mathbf{i}, \mathbf{j}, \mathbf{k}$

$|\mathbf{a} \cdot (\mathbf{b} \times \mathbf{c})|$

$a_y b_z - a_z b_y$