document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091437>Question 1091437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the angle between the given vectors to the nearest tenth of a degree. \r<BR>\n" );
document.write( "\n" );
document.write( "u = <-5, 8>, v = <-4, 8> </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #705850 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=705850\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the two expressions of the vector dot product:\r<BR>\n" );
document.write( "\n" );
document.write( " u • v =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+abs%28u%29%2Aabs%28v%29+%2A+cos%28theta%29+=+u%5Bx%5D%2Av%5Bx%5D+%2B+u%5By%5D%2Av%5By%5D+ ALIGN=MIDDLE  ALT=\"+abs%28u%29%2Aabs%28v%29+%2A+cos%28theta%29+=+u%5Bx%5D%2Av%5Bx%5D+%2B+u%5By%5D%2Av%5By%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "              <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+++cos%28theta%29+=+%28u%5Bx%5D%2Av%5Bx%5D+%2B+u%5By%5D%2Av%5By%5D%29%2F%28abs%28u%29%2Aabs%28v%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-5%29%28-8%29+%2B+%288%29%288%29%29+%2F+%28sqrt%28-5%5E2%2B8%5E2%29%2Asqrt%28-4%5E2%2B8%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++84+%2F+%28%289.43398%29%288.94427%29%29+ ALIGN=MIDDLE  ALT=\"++84+%2F+%28%289.43398%29%288.94427%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++84+%2F+84.38008+ ALIGN=MIDDLE  ALT=\"++84+%2F+84.38008+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++0.9955+ ALIGN=MIDDLE  ALT=\"++0.9955+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+theta+=+cos%5E-1%280.9955%29+=+highlight%28+5.4%5Eo+%29+ ALIGN=MIDDLE  ALT=\"+theta+=+cos%5E-1%280.9955%29+=+highlight%28+5.4%5Eo+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "—<BR>\n" );
document.write( "Check:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28-5%5E2%2B8%5E2%29%2Asqrt%28-4%5E2%2B8%5E2%29+cos%285.4%5Eo%29+=+9.43398%2A8.94427%2A0.9955+=+84.0+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > which you will recall is the dot product found by multiplying corresponding vector components <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+u%5Bx%5Dv%5Bx%5D+%2B+u%5By%5Dv%5By%5D+ ALIGN=MIDDLE  ALT=\"+u%5Bx%5Dv%5Bx%5D+%2B+u%5By%5Dv%5By%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );