Moderate# Angles with Coordinate Axes

MVCALC-IO4K5T

For each vector in this question, let $\alpha$, $\beta$, and $\gamma$ denote the angle that the vector makes with the unit vector ${\bf i}$, ${\bf j}$, and ${\bf k}$, respectively.

For which one of the five vectors is it true that $\cos \alpha +\cos \beta =\cos \gamma $?