# Illustration Vectors and vector components - orthogonal coordinate system

You see an orthogonal coordinate system with coordinates $$(x,~y,~z)$$ any two three-dimensional vectors $$\boldsymbol{a}$$ and $$\boldsymbol{b}$$ and their components:$\boldsymbol{a} ~=~ (a_1,~a_2,~a_3)$ $\boldsymbol{b} ~=~ (b_1,~b_2,~b_3)$
Here $$a_1$$ is the length of the vector $$\boldsymbol{a}$$ in the $$x$$-direction, $$a_2$$ is the length of the vector $$\boldsymbol{a}$$ in the $$y$$-direction, and $$a_3$$ is the length of the vector $$\boldsymbol{a}$$ in the $$z$$-direction. For the vector $$\boldsymbol{b}$$ this applies analogously.