when vectors to be added are not perpendicular, the method of addition by components described below can be used.

To add two or more vectors A, B, C ….. by the component method, the following procedure can be used

**1.** Resolve the initial vectors into components in the $x$, $y$, and $z$ directions.

**2.** Add the components in the $x$ direction to give $R_{x}$, add the components in the $y$ direction to give $R_{y}$, and add the components in the $z$ direction to give $R_{z}$. That is the magnitude of $R_{x}$, $R_{y}$ and $R_{z}$ are given by,

$R_{x}$ = $A_{x}+B_{x}+C_{x}+....$

$R_{y}$ = $A_{y}+B_{y}+C_{y}+....$

$R_{z}$ = $A_{z}+B_{z}+C_{z}+....$

**3. **Calculate the magnitude of the resultant R from its components $R_{x}$, $R_{y}$ and $R_{z}$ using the polygon theorem:

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