Magnitude & Direction (Edexcel A-Level Mathematics): Flashcards

$|a| = \sqrt{a_1^2 + a_2^2}$

$|a| = \sqrt{a_1^2 + a_2^2 + a_3^2}$

$\theta = \tan^{-1}(a_2/a_1)$

The length or size of the vector.

$\theta = \tan^{-1}(2/3) \approx 33.7°$

Magnitude = $\sqrt{2^2 + 3^2} = \sqrt{13}$

$\theta \approx 233.13°$ in quadrant III, calculated by arctan.

Magnitude = $\sqrt{(-2)^2 + (-4)^2} = \sqrt{20} = 2\sqrt{5}$

Coordinates: $(-1.5, 2.598)$ from $(3 \cos 120°, 3 \sin 120°)$

Magnitude and direction.