Vectors have magnitude (size) and direction.

$$\begin{array}{|c|c|c|} \hline \text{quantity} & \text{vector} & \text{scalar} \\ \hline \text{force} & \checkmark & \\ \hline \text{energy} & & \checkmark \\ \hline \text{velocity} & \checkmark & \\ \hline \text{speed} & & \checkmark \\ \hline \end{array}$$

Vectors have magnitude (size) and direction.

Any vector can be resolved into two perpendicular components.

In the example above the horizontal force is given by

$$ F_x = F\cos\theta $$

and

$$ F_y = F\sin\theta $$

The forces on an inclined plane are best resolved perpendicular and parallel to the plane.

In this example th component of weight along the inclined plane is given by

$$ F_{down plane} = F\sin 12\degree $$

and

$$ F_{perpendicular} = F\cos 12\degree $$

Use pythagoros to add perpendicular vectors

$$ F^2 = {F_x}^2 + {F_y}^2 $$

and use trigonometry to find the angle from North clockwise (bearing)

$$ \tan\theta = \frac{F_y}{F_x} $$