Element-Wise Multiplication and Division with Column Vector Variables

As ttokoro already had shown, what you are looking for is called "vectorization" in Mathcad and Prime.>

Vectorization is applied if you want a scalar calculation to be done with vectors element-wise. All involved vectors must have the same size and vectorization does not work recursively.

Prime applies vectorization automatically if the operation is not defined for vectors. So when v is a vector (in Prime only column vectors are considered vectors), Prime applies implicit vectorization if you type v² but uses the scalar vector product when you use v*v.

Exponentiation (and likewise division) is not defined for vectors, so instead of issuing an error message, Prime automatically applies vectorization. While this is a convenient approach, it also means that, as in the example below for a*a/b, one might initially assume that the calculation is being performed element by element and continue to compute with incorrect results.