document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=35500>Question 35500</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the vector u has magnitude 10 and bearing 200 degrees. vector v has magnitude 8 and bearing 35 degrees. choose the correct magnitude of u-v and its bearings. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #21664 by </B><A HREF=/tutors/aboutme.mpl?userid=narayaba><B>narayaba(40)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=narayaba><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=21664\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Vectors can be represneted in two possible ways. A vector can be represented using the cartesian cordinate system (x,y). They can also be represented as polar cordinates. In polar cordinate a vector is represented by its magnitude and its angle with respect to the positive direction of X axis. \r<BR>\n" );
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document.write( "If T is a vector with components (tx,ty) in cartesian cordinate system then in polar cordinate the vector can be written as follows\r<BR>\n" );
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document.write( "magnitude r = sqrt(tx^2 + ty^2) and angle theta  = tan^-1(ty/tx) (inverse tan)<BR>\n" );
document.write( "  here tx = r*cos(theta) and ty = r*sin(theta)  ------  EQUATION 1\r<BR>\n" );
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document.write( "now the vector T can be represented in polar cordinate as  (r,theta)\r<BR>\n" );
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document.write( "For the vector u with magnitude r =8 and theta =35<BR>\n" );
document.write( "the x and y components are ux = 8*cos(35) = 8* 0.8192 = 6.5536<BR>\n" );
document.write( "and uy =8*sin(35)  = 8* 0.5736 = 4.5586\r<BR>\n" );
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document.write( "similarly For the vector v with magnitude r =10 and theta =200<BR>\n" );
document.write( "the x and y components are vx = 10*cos(200) = 10* -0.9397 = -9.9397<BR>\n" );
document.write( "and vy =10*sin(200)  = 10*-0.3420 = -3.420 \r<BR>\n" );
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document.write( "we want vector u - v in cartesian coordinates (ux-vx, uy-vy) = (16.4933, 7.9786)\r<BR>\n" );
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document.write( "Using EQUATION 1 <BR>\n" );
document.write( "The vector u - v in polar cordinates is r = sqrt(16.4933^2 + 7.9786^2) = 18.3218 \r<BR>\n" );
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document.write( "and theta = tan^-1(7.9786/16.4933) = 25.8153 degrees <BR>\n" );
document.write( "The vector u - v  in polar coordinates is (18.3218, 25.8153)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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