document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=515354>Question 515354</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the angle between the vectors <-9,-7>and <2,-1> . Carry your intermediate computations to at least 4 decimal places. Round your final answer to the nearest degree. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #343924 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=343924\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The dot product of those vectors is equal to (-9)(2) + (-7)(-1) = -11. This is also equal to the product of the magnitudes times the cosine of the angle in between. Hence,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -11 = \sqrt{130}\sqrt{5}\cos{\theta}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \theta = \cos^{-1} \frac{-11}{\sqrt{130}\sqrt{5}} \approx 116\"> (degrees) </SPAN>\n" );
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