Recital Vector Dot Operations for Chemistry Students

I have been teaching physical chemistry to undergraduate students for several years now. I have observed that my interpretation of vector-matrix calculations and complex calculations has not been well received by the chemistry students. The traditional vector notation of adding an arrow on top of a variable and the matrix format work for students with vector and matrix-associated training backgrounds but are not well received by the students who have not seen it before.1 We have been using vector square calculations in these classes in many places. Thus, there is a need to introduce vector calculations, especially square vector calculations to these students. I have recommended the students watch outstanding YouTube channels such as 3Blue1Brown that visualize vector calculations. I am proposing here to introduce a form more like linear algebra that is more familiar to the students and focuses on the DOT operations of the vectors to these undergraduate students. Linearized vector notations have been widely used in almost all computer coding languages and have been proven to be efficient by many coders.