document.write( "Question 861264: Find 2u-3v, u+v, and 3u-4v for the given vectors u and v\r
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Algebra.Com's Answer #518945 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hi, there--\r\n" );
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document.write( "YOUR PROBLEM:\r\n" );
document.write( "Given the vectors\r\n" );
document.write( "u = (2,7) and\r\n" );
document.write( "v = (3,1)\r\n" );
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document.write( "Find 2u-3v, u+v, and 3u-4v\r\n" );
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document.write( "SOLUTION:\r\n" );
document.write( "To work add and subtract vectors, you work with the x-components and y-components separately.\r\n" );
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document.write( "(a) 2u-3v\r\n" );
document.write( "Multiply the x-component and the y-component of vector u by 2 to get the vector 2u. \r\n" );
document.write( "2u = (2*2,2*7) = (4,14)\r\n" );
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document.write( "Multiply both components of vector v by 3 to get vector 3v.\r\n" );
document.write( "3v = (3*3,3*1) = (9,3)\r\n" );
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document.write( "Now subtract the x- and y-compnents of  3v from those of 2u to get the components of 2u-3v.\r\n" );
document.write( "2u - 3v = (4-9,14-3) = (-5,11)\r\n" );
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document.write( "(b) u+v\r\n" );
document.write( "Add the x- and y-components of u and v separately to give the components of u+v.\r\n" );
document.write( "(u+v) = (2+3,7+1) = (5,8)\r\n" );
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document.write( "(c) 3u-4v\r\n" );
document.write( "3u = (3*2,3*7) = (6,21)\r\n" );
document.write( "4v = (4*3,4*1) = (12,4)\r\n" );
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document.write( "3u-4v = (6-12,21-4) = (-6,17)\r\n" );
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document.write( "I hope this helps. Feel free to email if you have questions about the explanation.\r\n" );
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document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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