document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205585>Question 205585</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi all, I cant seem to get this next problem sorted. I need to find the direction cosines of the vector:<BR>\n" );
document.write( "~w = 2~i - ~j + 5~k.<BR>\n" );
document.write( "(Again, the ~ symbols refer to arrows in the positive direction above each value, with ~ in-between referring to the arrow being above both values together)<BR>\n" );
document.write( "Any help with notes would be really good.<BR>\n" );
document.write( "Thanks, -Nick.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #155208 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=155208\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I need to find the direction cosines of the vector:<BR>\n" );
document.write( "w = 2i - j + 5k<BR>\n" );
document.write( "The 3 direction cosines are the cosines of the angles between the vector and the x, y and z-axes.<BR>\n" );
document.write( "Find the dot product of w with a unit vector along each axis.<BR>\n" );
document.write( "Angle A = x cos<BR>\n" );
document.write( "Angle B = y cos<BR>\n" );
document.write( "Angle C = z cos<BR>\n" );
document.write( "------<BR>\n" );
document.write( "w dot x = |2 -1 5||1 0 0| = 2<BR>\n" );
document.write( "2 = |w|*|x|cos(x)<BR>\n" );
document.write( "|w| = sqrt(4+1+25) = sqrt(30)<BR>\n" );
document.write( "cos(x) = 2/sqrt(30) x direction cosine<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "w dot y = |2 -1 5||0 1 0| = -1<BR>\n" );
document.write( "cos(y) = -1/sqrt(30) y cosine<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "w dot z = |2 -1 5||0 0 1| = 5<BR>\n" );
document.write( "cos(z) = 5/sqrt(30) z cosine<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );