document.write( "Question 1189550: if A=2i+4j+k and B=4i+2j+k find the vector x parallel to A and have magnitude of B? \n" ); document.write( "
Algebra.Com's Answer #820934 by ikleyn(52787)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "if A=2i+4j+k and B=4i+2j+k find the vector x parallel to A and have magnitude of B?
\n" ); document.write( "~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Notice that vectors A and B have THE SAME magnitude\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    |A| = \"sqrt%282%5E2%2B4%5E2%2B1%5E2%29\" = \"sqrt%284%2B16%2B1%29\" = \"sqrt%2817%29\",\r\n" );
document.write( "\r\n" );
document.write( "    |B| = \"sqrt%284%5E2%2B2%5E2%2B1%5E2%29\" = \"sqrt%2816%2B4%2B1%29\" = \"sqrt%2817%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus, the problem asks to find vector x parallel to A and having the same magnitude as A.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "There is ONLY ONE such a vector: it is vector A itself.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  There is ONLY ONE such a vector: it is vector A itself.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved and explained.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

Post-solution note

: \r
\n" ); document.write( "\n" ); document.write( "        In my solution,  I do not consider  ANTI-parallel vector  -A  as a parallel to  A.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );