単位ベクトル
| r | = x 2 + y 2 + z 2 {\displaystyle |{\boldsymbol {r}}|={\sqrt {x^{2}+y^{2}+z^{2}}}}
となるから、 r ^ {\displaystyle {\hat {\boldsymbol {r}}}} の i, j, k への分解は
r ^ = 1 | r | ( x i + y j + z k ) = x x 2 + y 2 + z 2 i + y x 2 + y 2 + z 2 j + z x 2 + y 2 + z 2 k {\displaystyle {\begin{aligned}{\hat {\boldsymbol {r}}}&={\frac {1}{|{\boldsymbol {r}}|}}(x{\boldsymbol {i}}+y{\boldsymbol {j}}+z{\boldsymbol {k}})\\&={\frac {x}{\sqrt {x^{2}+y^{2}+z^{2}}}}{\boldsymbol {i}}+{\frac {y}{\sqrt {x^{2}+y^{2}+z^{2}}}}{\boldsymbol {j}}+{\frac {z}{\sqrt {x^{2}+y^{2}+z^{2}}}}{\boldsymbol {k}}\end{aligned}}}