document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=824359>Question 824359</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Add the following vectors:\r<BR>\n" );
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document.write( "A=352, Angle A=184 degrees and B=283, Angle B=348 degrees\r<BR>\n" );
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document.write( "Can you please help me solve this and show me step by step how to work it? Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #496393 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=496393\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can find the x and y components<BR>\n" );
document.write( "of each vector, then add x's, then<BR>\n" );
document.write( "add y's. The vector sum can then be found<BR>\n" );
document.write( "------------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bx%5D+=+-A%2Acos%284%29+ ALIGN=MIDDLE  ALT=\"+A%5Bx%5D+=+-A%2Acos%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5By%5D+=+-A%2Asin%284%29+ ALIGN=MIDDLE  ALT=\"+A%5By%5D+=+-A%2Asin%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Note that 184 degrees is in the 3rd<BR>\n" );
document.write( "quadrant where both sin and cos are negative<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+184+-+180+=+4+ ALIGN=MIDDLE  ALT=\"+184+-+180+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the angle the<BR>\n" );
document.write( "vector makes with the x-axis<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+B%5Bx%5D+=+B%2Acos%2812%29+ ALIGN=MIDDLE  ALT=\"+B%5Bx%5D+=+B%2Acos%2812%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+B%5By%5D+=+-B%2Asin%2812%29+ ALIGN=MIDDLE  ALT=\"+B%5By%5D+=+-B%2Asin%2812%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "Vector B is in the 4th quadrant where<BR>\n" );
document.write( "the cos is positive and sin is negative<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+360+-+348+=+12+ ALIGN=MIDDLE  ALT=\"+360+-+348+=+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the angle B<BR>\n" );
document.write( "makes with the x-axis<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bx%5D+%2B+B%5Bx%5D+=+-A%2Acos%284%29+%2B+B%2Acos%2812%29+ ALIGN=MIDDLE  ALT=\"+A%5Bx%5D+%2B+B%5Bx%5D+=+-A%2Acos%284%29+%2B+B%2Acos%2812%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bx%5D+%2B+B%5Bx%5D+=+-352%2A.9976+%2B+283%2A.9781+ ALIGN=MIDDLE  ALT=\"+A%5Bx%5D+%2B+B%5Bx%5D+=+-352%2A.9976+%2B+283%2A.9781+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bx%5D+%2B+B%5Bx%5D+=+-351.1552+%2B+276.8023+ ALIGN=MIDDLE  ALT=\"+A%5Bx%5D+%2B+B%5Bx%5D+=+-351.1552+%2B+276.8023+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bx%5D+%2B+B%5Bx%5D+=+-74.3529+ ALIGN=MIDDLE  ALT=\"+A%5Bx%5D+%2B+B%5Bx%5D+=+-74.3529+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5By%5D+%2B+B%5By%5D+=+-A%2Asin%284%29+-+B%2Asin%2812%29+ ALIGN=MIDDLE  ALT=\"+A%5By%5D+%2B+B%5By%5D+=+-A%2Asin%284%29+-+B%2Asin%2812%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5By%5D+%2B+B%5By%5D+=+-352%2A.0698+-+283%2A.2079+ ALIGN=MIDDLE  ALT=\"+A%5By%5D+%2B+B%5By%5D+=+-352%2A.0698+-+283%2A.2079+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5By%5D+%2B+B%5By%5D+=+-24.5696+-+58.8357+ ALIGN=MIDDLE  ALT=\"+A%5By%5D+%2B+B%5By%5D+=+-24.5696+-+58.8357+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5By%5D+%2B+B%5By%5D+=+-83.4053+ ALIGN=MIDDLE  ALT=\"+A%5By%5D+%2B+B%5By%5D+=+-83.4053+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "These magnitudes both being negative means <BR>\n" );
document.write( "the resultant vector is in the 3rd quadrant<BR>\n" );
document.write( "Call the resultant vector <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+ ALIGN=MIDDLE  ALT=\"+C+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5E2+=+%28+-74.3529+%29%5E2+%2B+%28+-83.4053+%29%5E2+ ALIGN=MIDDLE  ALT=\"+C%5E2+=+%28+-74.3529+%29%5E2+%2B+%28+-83.4053+%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5E2+=+5528.3537+%2B+6956.4441+ ALIGN=MIDDLE  ALT=\"+C%5E2+=+5528.3537+%2B+6956.4441+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5E2+=+12484.7978+ ALIGN=MIDDLE  ALT=\"+C%5E2+=+12484.7978+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+abs%28+C+%29+=+111.7354+ ALIGN=MIDDLE  ALT=\"+abs%28+C+%29+=+111.7354+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the magnitude of the resultant vector, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+ ALIGN=MIDDLE  ALT=\"+C+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "The angle, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the x-axis is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28a%29+=+74.3529+%2F+83.4053+ ALIGN=MIDDLE  ALT=\"+cos%28a%29+=+74.3529+%2F+83.4053+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28a%29+=+.8915+ ALIGN=MIDDLE  ALT=\"+cos%28a%29+=+.8915+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+26.9377+ ALIGN=MIDDLE  ALT=\"+a+=+26.9377+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This angle is in the 3rd quadrant, so I have<BR>\n" );
document.write( "to add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+180+ ALIGN=MIDDLE  ALT=\"+180+\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+180+=+26.9377+%2B+180+ ALIGN=MIDDLE  ALT=\"+a+%2B+180+=+26.9377+%2B+180+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+180+=+206.9377+ ALIGN=MIDDLE  ALT=\"+a+%2B+180+=+206.9377+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "So, the answer is:<BR>\n" );
document.write( "111.7354 angle 206.9377<BR>\n" );
document.write( "Unless I made an error ( very possible )<BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "This method always works. you might be asked<BR>\n" );
document.write( "to do it a different way, but the result<BR>\n" );
document.write( "should be the same<BR>\n" );
document.write( "hope this helps<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );