Is 1/vector is a vector or not?

Question

Let $\vec { A } = a \hat { i } + b \hat { j } + c \hat { k }$. Is $\frac { 1 } { \vec { A } }$ a vector or not, and if it is, then what are its components?"

Answer 1

There is no standard definition of $\frac{1}{\boldsymbol{x}}$ where $\boldsymbol{x}$ is a vector. Therefore, the expression "$\frac{1}{\boldsymbol{x}}$" is generally meaningless (undefined), unless it is specifically defined in the context where it is used.