document.write( "Question 1202643: given that a=2i+3j-k, b=i-j+2k, and c=3i+4j+k, find (a) a+2b-c, (b) a vector d such that a+b+c+d=0, and (c) a vector d such that a-b+c+3d=0 \n" ); document.write( "
Algebra.Com's Answer #837620 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I think you'll find that it's easier to use the < p,q,r > notation in\r\n" );
document.write( "vector calculus than the pi+qj+rk notation.  Otherwise, you are likely\r\n" );
document.write( "to get letters used for vectors and letters used for scalars confused.\r\n" );
document.write( "Ordinary letters are used for scalars and letters in bold-face italics are used\r\n" );
document.write( "for vectors.  The < p,q,r > avoids having to use so many bold-face italic\r\n" );
document.write( "letters.\r\n" );
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document.write( "given that a=2l+3j-k, b=l-j+2k, and c=3l+4j+k, find\r\n" );
document.write( "(a) a+2b-c\r\n" );
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document.write( "a = < 2,3,-1 >, b = < 1,-1,2 >, c = < 3,4,1 >\r\n" );
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document.write( "a+2b-c = < 2,3,-1 > + 2< 1,-1,2 > - < 3,4,1 > =\r\n" );
document.write( "         < 2,3,-1 > + < 2,-2,4 > + < -3,-4,-1 > =\r\n" );
document.write( "         < 2+2-3,3-2-4,-1+4-1 > = < 1,-3,2 > = l-3j+2k\r\n" );
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document.write( "(b) a vector d such that a+b+c+d=0,\r\n" );
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document.write( "Let d = pl+qj+rk = < p,q,r >\r\n" );
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document.write( "a+b+c+d = < 2,3,-1 > + < 1,-1,2 > + < 3,4,1 > + < p,q,r > = 0 = < 0,0,0 >\r\n" );
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document.write( "          < 2+1+3+p,3-1+4+q,-1+2+1+r > = < 0,0,0 >\r\n" );
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document.write( "               < 6+p,6+q,2+r > = < 0,0,0 >\r\n" );
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document.write( "                6+p=0;   6+q=0;   2+r=0\r\n" );
document.write( "                  p=-6;    q=-6;    r=-2\r\n" );
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document.write( "d = pl+qj+rk = < p,q,r > = < -6,-6,-2 >\r\n" );
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document.write( "and (c) a vector d such that a-b+c+3d=0\r\n" );
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document.write( "Let d = pl+qj+rk = < p,q,r >\r\n" );
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document.write( "a-b+c+3d = < 2,3,-1 > - < 1,-1,2 > + < 3,4,1 > + 3< p,q,r > = 0 = < 0,0,0 >\r\n" );
document.write( "         = < 2,3,-1 > + < -1,1,-2 > + < 3,4,1 > + < 3p,3q,3r > = 0 = < 0,0,0 >\r\n" );
document.write( "          < 2-1+3+3p,3+1+4+3q,-1-2+1+3r > = < 0,0,0 >\r\n" );
document.write( "           < 4+3p,8+3q,-3+3r > = < 0,0,0 >\r\n" );
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document.write( "                4+3p=0;   8+3q=0;   -2+3r=0\r\n" );
document.write( "                  3p=-4;    3q=-8;     3r=2\r\n" );
document.write( "                   p=-4/3;   q=-8/3;    r=2/3\r\n" );
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document.write( "d = pl+qj+rk = < p,q,r > = < -4/3,-8/3,2/3 >\r\n" );
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document.write( "Edwin
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