It is made an attempt to discover an explainable plausible reason for the existence of the conditions of optimality for Cartesian vector direction cosines, having importance in energy mechanical engineering, with the help of the multi-optional hybrid functions entropy conditional optimality doctrine. Substantiation is made in terms of the calculus of variations theory with the help of the special hybridoptional effectiveness functions uncertainty measure, which includes the hybrid functions

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... opy of the traditional Shannon's style. In the studied cases, the simplest variational problems solutions, which are the numbers known as the direction cosines of a Cartesian vector, are stipulated by the specified natural logarithmic quadratic forms. It is proposed to evaluate the uncertainty/certainty degree of the magnitude and direction of a Cartesian vector with the use of the objective functional. This is a new insight into the scientific explanation of the well-known dependency derived in another way. The developed theoretical contemplations and mathematical derivations are finalized with a simplest numerical example for the variated value of the multi-optional hybrid function resulting in the objective functional.