The addition of a third dimension alters the process of [[Vector|vector]] decomposition of an arbitrary [[Force|force]] slightly: $F_x=F\cos⁡\theta_x$ $F_y=F\cos⁡\theta_y$ $F_z=F\cos⁡\theta_z$ $F=\sqrt{F_x^2+F_y^2+F_z^2}$ $\vec{F}=F_x​\hat{i}+F_y\hat{​j}​+F_z\hat{​k}$ $\vec{F}=F(\cos\theta_x\hat{​i}+\cos\theta_y\hat{​j}​+\cos\theta_z\hat{​k})$ We can describe the vector component of the last equation with respect to the forces [[Unit Vector|unit vector]]: $F(\cos\theta_x\hat{​i}+\cos\theta_y\hat{​j}​+\cos\theta_z\hat{​k})=F\hat{n}$