Working with Vectors (AQA A-Level Mathematics): Flashcards

Quantities with magnitude and direction

$A_x = A \cos \theta$

$A_y = A \sin \theta$

$\vec{R} = (A_x + B_x) \hat{i} + (A_y + B_y) \hat{j}$

$|\vec{A}| = \sqrt{A_x^2 + A_y^2}$

$\theta = \tan^{-1} \left(\frac{A_y}{A_x}\right)$

$\vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos \theta$

$\vec{A} \cdot \vec{B} = A_x B_x + A_y B_y$

$|\vec{A} \times \vec{B}| = |\vec{A}| |\vec{B}| \sin \theta$

Resultant force is zero: $\sum \vec{F} = \vec{0}$