document.write( "Question 1206230: A vector has magnitude 6.0 units due east, vector B points due north. Find
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Algebra.Com's Answer #843516 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A vector has magnitude 6.0 units due east, vector B points due north. Find
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\n" ); document.write( "b) the magnitude of A+B
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\n" ); document.write( "\n" ); document.write( "        In this post, first sentence is incorrect. Instead of \" A vector has magnitude 6.0 units due east, . . . \"
\n" ); document.write( "       should be \" Vector A has magnitude 6.0 units due east, . . . \".\r
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\n" ); document.write( "\n" ); document.write( "       It may seems like a small microscopic thing, but in Math every word matters, and the order
\n" ); document.write( "        of the words does matters, too. Wrong order of words makes the post non-sensical.\r
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\n" ); document.write( "\n" ); document.write( "        So, I will solve the problem, edited this way.\r
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document.write( "(a)  Since in the coordinate plane vector A is vertical and vector B is horizontal, \r\n" );
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document.write( "     vector A+B has x-component Ax = 6 = |A|, the magnitude of vector A, \r\n" );
document.write( "            and has y-component |B|, the magnitude of vector B.\r\n" );
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document.write( "     Since tan(60°) = ,  it implies that   = .\r\n" );
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document.write( "     From this equation, we get |B| =  = 10.3923  (rounded).\r\n" );
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document.write( "     It gives the ANSWER to question (a) :  the magnitude of vector B is   = 10.3923  (rounded).\r\n" );
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document.write( "(b)  Now we know that x-component of vector A+B is the same as x-component of vector A, i.e. 6,\r\n" );
document.write( "     and we know that y-component of vector A+B is the same as y-component of vector B, i.e. .\r\n" );
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document.write( "     Hence, the magnitude of A+B is   =  =  = 2*6 = 12.\r\n" );
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document.write( "     It gives the ANSWER to question (b) :  the magnitude of A+B is 12.\r\n" );
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