document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183181>Question 1183181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Each of angles b/t the vectors u,v,& w is 60. ||u||= 4. . ||v||=2 & ||w||=6<BR>\n" );
document.write( "Then find ||u+v+w||<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813383 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813383\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the fact that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28u%29%5E2+=+u%2Au+ ALIGN=MIDDLE  ALT=\"abs%28u%29%5E2+=+u%2Au+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%2Av+=+abs%28u%29abs%28v%29cos%28theta%29 ALIGN=MIDDLE  ALT=\"u%2Av+=+abs%28u%29abs%28v%29cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28u%29 ALIGN=MIDDLE  ALT=\"abs%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the magnitude of the vector <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%2Av ALIGN=MIDDLE  ALT=\"u%2Av\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the dot product of the vectors <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v ALIGN=MIDDLE  ALT=\"v\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28u%2Bv%2Bw%29%5E2+=+%28u%2Bv%2Bw%29%2A%28u%2Bv%2Bw%29%0D%0A%0D%0A=+u%2Au+%2B+v%2Av+%2B+w%2Aw+%2B+2%28u%2Av+%2B+v%2Aw+%2B+u%2Aw%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, by direct application of the distributive, commutative, and associative properties.\r<BR>\n" );
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document.write( "Now \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%2Au+%2B+v%2Av+%2B+w%2Aw+%2B+2%28u%2Av+%2B+v%2Aw+%2B+u%2Aw%29+=+abs%28u%29%5E2+%2B+abs%28v%29%5E2+%2B+abs%28w%29%5E2+%2B+2%28abs%28u%29%2Aabs%28v%29cos%28theta%5B1%5D%29+%2B+abs%28v%29%2Aabs%28w%29cos%28theta%5B2%5D%29+%2B+abs%28u%29%2Aabs%28w%29cos%28theta%5B3%5D%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28u%29%5E2+%2B+abs%28v%29%5E2+%2B+abs%28w%29%5E2+%2B+2%28abs%28u%29%2Aabs%28v%29cos60%5E0+%2B+abs%28v%29%2Aabs%28w%29cos60%5E0+%2B+abs%28u%29%2Aabs%28w%29cos60%5E0%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta%5B1%5D+=+theta%5B2%5D+=+theta%5B3%5D+=+60%5E0 ALIGN=MIDDLE  ALT=\"theta%5B1%5D+=+theta%5B2%5D+=+theta%5B3%5D+=+60%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28u%29%5E2+%2B+abs%28v%29%5E2+%2B+abs%28w%29%5E2+%2B+abs%28u%29%2Aabs%28v%29+%2B+abs%28v%29%2Aabs%28w%29+%2B+abs%28u%29%2Aabs%28w%29++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos60%5E0+=+1%2F2 ALIGN=MIDDLE  ALT=\"cos60%5E0+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "= 16 + 4 + 36 + 8 + 12 + 24 = 100.\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28u%2Bv%2Bw%29%5E2+=+100 ALIGN=MIDDLE  ALT=\"abs%28u%2Bv%2Bw%29%5E2+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28abs%28u%2Bv%2Bw%29+=+10%29 ALIGN=MIDDLE  ALT=\"highlight%28abs%28u%2Bv%2Bw%29+=+10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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