document.write( "Question 1206236: Prove that two vectors must have equal magnitudes if their sum is perpendicular to their difference \n" ); document.write( "
Algebra.Com's Answer #843528 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "Geometrically, the sum of two vectors is a DIAGONAL of the parallelogram, built on these vectors as on consecutive sides.\r
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\n" ); document.write( "\n" ); document.write( "Then the difference of the vectors is the OTHER DIAGONAL of the same parallelogram, built on these vectors as on consecutive sides.\r
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\n" ); document.write( "\n" ); document.write( "If the sum of two vectors is perpendicular to their difference, it means that
\n" ); document.write( "the diagonals of the parallelogram are perpendicular.\r
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\n" ); document.write( "\n" ); document.write( "But if a parallelogram has perpendicular diagonals, then this parallelogram is a rhombus,
\n" ); document.write( "and, hence, all his sides have equal lengths.\r
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\n" ); document.write( "\n" ); document.write( "It is a geometric proof of your statement.\r
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\n" ); document.write( "\n" ); document.write( "At this point, this geometric proof is complete.\r
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