Final answer:
The intersection of planes ABG and BCD is the line segment 'B'. As planes intersect in a line and based on the provided labels, 'B' is the intersecting line segment common to both planes.
Step-by-step explanation:
The intersection of planes ABG and BCD is best determined by identifying the line segment or edge that both planes share. Although the detailed breakdown of the figure is not provided, based on the labeling of the planes, it can be inferred that the segment line 'B' is common to both planes ABG and BCD. Thus, the intersection of planes ABG and BCD would logically be line segment 'B'.
In general, when two planes intersect in three-dimensional space, their intersection is a line. If we had a specific diagram or a description of a three-dimensional shape with labeled vertices, we could provide a more detailed explanation of the intersection using that context. As for the operations involving vectors mentioned in the examples, such as showing that (B x C) . A being the volume of a parallelepiped or finding vector sums and products, they illustrate different mathematical computations applied to geometrical contexts and vector analysis.