A Geometric Implication

Geometry Level 5

Let $$P_{1}$$ be a plane determined by the vectors $$A$$ and $$B$$. Plane $$P_{2}$$ be determined by vectors $$C$$ and $$D$$. Plane $$P_{3}$$ be determined by vectors $$A$$ and $$C$$. Plane $$P_{4}$$ be determined by vectors $$B$$ and $$D$$. If $$L_{1}$$ represents the line of intersection (direction) of planes $$P_{1}$$ and $$P_{2}$$, and $$L_{2}$$ represents the line of intersection(direction) of $$P_{3}$$ and $$P_{4}$$. The vector along the direction of $$L_{1} \times L_{2}$$ is given by,

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