The sum difference and cross products of a two vectors a and b
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Since A and B are perpendicular and equal in size, A + B and A - B form the two diagonal lines of a square with A and B its two adjacent sides, therefore A + B and A - B are perpendicular.
A x B is perpendicular to the plane formed by A + B and A - B, hence A x B is perpendicular to both A + B and A - B
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