Refresher - Resolving Vectors Into Components

Resolving vectors into their components

We will often have to break are vectors down to their components:

Adding vectors using components

1st step:

Draw each individual vector in a separate coordinate system, and label them.
Find the “ x and y “ component of each vector.
Add all of the x-components of all of the vectors to find the resultant x-component, Rx. Do the same to find the resultant y-component, Ry.

$R_{x} = A_{x} + B_{x} + \dots$

$R_{y} = A_{y} + B_{y} + \dots$

2^nd step:

$R = \sqrt{R_{x}^{2} + R_{y}^{2}}$

Use a suitable trigonometric function to find the angle the resultant vector makes with the x-axis.

$T a n θ = (\frac{R_{y}}{R_{x}})$

Different ways of describing a vector:

Using components:

$A = A_{x} + A_{y} + A_{z}$
$A_{x} = (A_{x}) i \to (A cos θ) i$
$A_{y} = (A_{y}) j \to (A sin θ) j$