document.write( "Question 364482: Hi,
\n" ); document.write( "Im Struggeling with this question:\r
\n" ); document.write( "\n" ); document.write( "Vectors:\r
\n" ); document.write( "\n" ); document.write( "Show that vectors a = 2i-4j-k, b = 3i+2j-2k and c = 5i-2j-3k can form the sides of a triangle, find the length of each side and hence show that the triangle has a right angle. sketch the triangle of vectors, indicating their directions and the right angle,\r
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\n" ); document.write( "Scott \n" ); document.write( "

Algebra.Com's Answer #759806 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "If three vectors \"a\", \"b\" and \"c\" are given (in  or in  , it does not matter),\r\n" );
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document.write( "then the necessary and sufficient condition for them to be the sides of a triangle / (to form a triangle) is the equality\r\n" );
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document.write( "    a + b + c = 0.\r\n" );
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document.write( "You can EASILY check ON YOUR OWN that for the given vectors\r\n" );
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document.write( "    a + b - c = 0.\r\n" );
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document.write( "It means that the vectors \"a\", \"b\" and \"-c\" form a triangle;\r\n" );
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document.write( "hence, the segments \"a\", \"b\" and \"c\" (if you forget about their directions) form a triangle.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The second part of the proof, regarding right angle triangle, do in the same way as the other author did in his (or her) post.\r
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( " - Sum of vectors that are coherently oriented sides of a convex closed polygon \r
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