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Vector components

A vector $\vec a$ has both magnitude and direction, and can be split into an x- and a y-component. This makes it easy to add several vectors: add the components separately.

\vec a = (a_x, a_y)

component form

|\vec a| = \sqrt{a_x^2+a_y^2}

magnitude of the vector

a_x = |\vec a|\cos\theta,\ a_y = |\vec a|\sin\theta

components from magnitude and angle

Symbols

$a_x,\ a_y$	components
$\theta$	angle from the x-axis	°

Example

A vector of length 10 at angle $37^\circ$ : $a_x=10\cos37^\circ\approx 7.99$ and $a_y=10\sin37^\circ\approx 6.02$ .

Vectors are added by adding the components, never by adding the magnitudes directly.

Practise vectors for free →

← The law of sines and cosines · The dot product →

Part of Foundations of Mathematics: Vectors.