document.write( "Question 475562: Hello. I need to find an x such that <5,6> and <2,3x> are a)parallel, b)orthogonal, and c)neither. How do i do this? \n" ); document.write( "

Algebra.Com's Answer #326148 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "<5,6> and <2,3x>\r\n" );
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document.write( "To be parallel one must be a multiple of the other:\r\n" );
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document.write( "<5,6> = k<2,3x>\r\n" );
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document.write( "<5,6> = <2k,3kx>\r\n" );
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document.write( "For the first equation k = \r\n" );
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document.write( "Substitute in the second equation:\r\n" );
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document.write( "6 = 3()x\r\n" );
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document.write( "12 = 3(5x)\r\n" );
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document.write( "12 = 15x\r\n" );
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document.write( " = x\r\n" );
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document.write( " = x\r\n" );
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document.write( "--------------------------\r\n" );
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document.write( "<5,6> and <2,3x>\r\n" );
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document.write( "To be orthogonal their dot product must be 0:\r\n" );
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document.write( "  <5,6>•<2,3x> = 0\r\n" );
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document.write( "(5)(2)+(6)(3x) = 0\r\n" );
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document.write( "        10+18x = 0\r\n" );
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document.write( "           18x = -10\r\n" );
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document.write( "             x = \r\n" );
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document.write( "             x = \r\n" );
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document.write( "----------------------------------\r\n" );
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document.write( "To be neither, choose x as anything other than those two values.\r\n" );
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document.write( "Edwin

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