document.write( "Question 1011206: Find a vector perpendicular to the given vector <5,-7,-8>
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Algebra.Com's Answer #626798 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Two non-zero vectors are perpendicular when\r\n" );
document.write( "their dot product is zero.  \r\n" );
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document.write( "Let < x,y,z > be a vector perpendicular to <5,-7,-8>. \r\n" );
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document.write( "Then,\r\n" );
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document.write( "<5,-7,-8> ∙ < x,y,z > = 5x-7y-8z = 0\r\n" );
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document.write( "We can pick any values of x,y, and z that\r\n" );
document.write( "will make the dot product above be 0.\r\n" );
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document.write( "For instance, since -8-7 =-15 and we can\r\n" );
document.write( "make the 5 become a +15 to cancel that by \r\n" );
document.write( "multiplying it by 3, so one solution would \r\n" );
document.write( "be to choose y and z to be 1 each and x to\r\n" );
document.write( "be 3.\r\n" );
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document.write( "So \r\n" );
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document.write( "<5,-7,-8> ∙ <3,1,1> = (5)(3)+(-7)(1)+(-8)(1)\r\n" );
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document.write( "= 15-7-8 = 0\r\n" );
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document.write( "So <3,1,1> is perpendicular to <5,-7,-8>\r\n" );
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document.write( "There are many other possibilities.\r\n" );
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document.write( "Edwin
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