Express each force vector in component form.

Step 1: Express each force vector in component form.
A force vector $\vec{F}$ with magnitude $M$ acting along the direction of a vector $\vec{v}$ is given by $\vec{F} = M \frac{\vec{v}}{|\vec{v}|}$.

For the first force, $\vec{F_1}$:
Magnitude $M_1 = 9\sqrt{3}$ N
Direction vector $\vec{v_1} = \vec{i} + 3\vec{j}$
Magnitude of direction vector $|\vec{v_1}| = \sqrt{1^2 + 3^2} = \sqrt{1+9} = \sqrt{10}$

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