### 2D Force Representation

$F_{x} =Fcos(θ)$ $F_{y} =Fsin(θ)$

### 3D Force Representation

#### Steps

- Determine the position vector from TAIL to HEAD of the force, labeled $AB$
- Determine the unit vector along the position vector, by dividing each of the components of the position vector by the norm of the position vector

$e_{AB}=∣AB∣AB $

- Determine the force vector, by multiplying the norm (magnitude) of the force by the unit vector

$F_{AB} =∣F∣e_{AB}$

##### PDF Visual Example

#### Other method, Use Projections with Dot Product

I really didn’t get this, because I didn’t really understand the dot product well.

By definition, the dot product is $F⋅Q =∣F∣∣Q ∣cosθ$

This helped me wrap my head around it Project Force F in the Q direction.

$u=∣Q ∣Q $

$F⋅u=∣F∣∣u∣cosθ=∣F∣cosθ$