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Originally Posted by Brian3.
Simple algebra:
XX > XY within the limits of any relationship.
He just had to find a way of making Y > X.
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Ah, grasshopper, but you seek the answer to the wrong question. X and Y are vectors!
The (scalar) dot products of X.X and X.Y may well be such that XX is greater than XY, but the (vector)
cross products tell a different story:
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In mathematics, the cross product or vector product is a binary operation on two vectors in three-dimensional space. It results in a vector which is perpendicular to both and therefore normal to the plane containing them. It has many applications in mathematics, physics, and engineering.
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Now, note that:
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the magnitude of the product equals the area of a parallelogram with the vectors for sides;
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But, most particularly, also note that:
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If the vectors have the same direction ... then their cross product is zero.
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So, the product of the X and Y vectors will, whilst being orthogonal to the X-Y plane, have a positive magnitude. But the product of the two X vectors will be zero!
In the real world of 3-Dimensional space, XY > XX, always.
