document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=539229>Question 539229</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the magnitude and direction (in degrees) of the vector.<BR>\n" );
document.write( "v = 3i +&#8730;7j </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #353359 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=353359\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If v = ai+bj, then ||v|| = sqrt(a^2+b^2)\r<BR>\n" );
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document.write( "In this case, a = 3 and b = sqrt(7)\r<BR>\n" );
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document.write( "||v|| = sqrt(a^2+b^2)\r<BR>\n" );
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document.write( "||v|| = sqrt(3^2+(sqrt(7))^2)\r<BR>\n" );
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document.write( "||v|| = sqrt(9+7)\r<BR>\n" );
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document.write( "||v|| = sqrt(16)\r<BR>\n" );
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document.write( "||v|| = 4\r<BR>\n" );
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document.write( "So the magnitude of v is 4\r<BR>\n" );
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document.write( "To find the direction or angle, we use the idea that theta = arctan(b/a)\r<BR>\n" );
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document.write( "theta = arctan(b/a)\r<BR>\n" );
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document.write( "theta = arctan(sqrt(7)/3)\r<BR>\n" );
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document.write( "theta = 41.409622 (note: this is approximate)\r<BR>\n" );
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document.write( "So the direction is roughly 41.409622 degrees.<BR>\n" );
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