document.write( "Question 1075449: Given vectors:
\n" ); document.write( "OP = <4,1,-6>
\n" ); document.write( "OQ = <2,-7,5>
\n" ); document.write( "OR = <3,-2,4>\r
\n" ); document.write( "\n" ); document.write( "Find the scalar n in OP+nOQ that is perpendicular to OR.\r
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Algebra.Com's Answer #690111 by Edwin McCravy(20056) $\"\"$ $\"About$

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Given vectors:
\n" ); document.write( "OP = <4,1,-6>
\n" ); document.write( "OQ = <2,-7,5>
\n" ); document.write( "OR = <3,-2,4>\r
\n" ); document.write( "\n" ); document.write( "Find the scalar n in OP+nOQ that is perpendicular to OR.
\n" ); document.write( "

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document.write( "OP+nOQ = <4,1,-6> + n<2,-7,5> = <4,1,-6> + <2n,-7n,5n> =\r\n" );
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document.write( "<4+2n,1-7n,-6+5n>\r\n" );
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document.write( "Two vectors are perpendicular if and only if their scalar \r\n" );
document.write( "(dot)-product is 0, so we set the dot product (OP+nOQ)•OR = 0, \r\n" );
document.write( "or \r\n" );
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document.write( "<4+2n,1-7n,-6+5n>•<3,-2,4> = 3(4+2n)-2(1-7n)+4(-6+5n) =\r\n" );
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document.write( "                                   12+6n-2+14n-24+20n = 0\r\n" );
document.write( "                                              -14+40n = 0\r\n" );
document.write( "                                                  40n = 14\r\n" );
document.write( "                                                    n = 14/40\r\n" );
document.write( "                                                    n = 7/20\r\n" );
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document.write( "Edwin

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