document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204887>Question 204887</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi all, Im still having trouble with these vector problems, I cant solve the problems listed below for the following: <BR>\n" );
document.write( "Let ~u = 3~i - ~j - 2~k and ~v = 2~i + ~j + ~k.(Again, the ~ symbols mean that there is and arrow symbol above the value in the positive direction)<BR>\n" );
document.write( "I need to:<BR>\n" );
document.write( "a) Find the corresponding unit vectors for ~u and ~v<BR>\n" );
document.write( "b) Calculate the dot product of the angle between ~u and ~v.<BR>\n" );
document.write( "Some help with steps and explanations on how to solve would be great.<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 #154701 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=154701\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let ~u = 3~i - ~j - 2~k and ~v = 2~i + ~j + ~k.(Again, the ~ symbols mean that there is and arrow symbol above the value in the positive direction)<BR>\n" );
document.write( "I need to:<BR>\n" );
document.write( "a) Find the corresponding unit vectors for ~u and ~v<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Find the magnitude of each.<BR>\n" );
document.write( "for u: = sqrt(9 + 1 + 4) = sqrt(14)<BR>\n" );
document.write( "Divide the vector by its magnitude to get the unit vector.<BR>\n" );
document.write( "--> 3i/sqrt(14) - j/sqrt(14) - 2k/sqrt(14)<BR>\n" );
document.write( "You can manipulate it to get the radical out of the denominators, or not.<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "for v: = sqrt(4 + 1 + 1)<BR>\n" );
document.write( "= sqrt(6)<BR>\n" );
document.write( "Same as above.<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "b) Calculate the dot product of the angle between ~u and ~v.<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "It's not the dot product of the angle.<BR>\n" );
document.write( "I assume you want to find the angle between the 2 vectors.<BR>\n" );
document.write( "Find the dot product:<BR>\n" );
document.write( "Multiply the i, j, and k elements, and add them.<BR>\n" );
document.write( "u dot v = 3*2 + -1*1 + -2*1 = 6-1-2 = 3<BR>\n" );
document.write( "The dot product is the product of the 2 magnitudes times the cos of the angle between them.  So the cos is<BR>\n" );
document.write( "dot/Mag(u)*Mag(v)<BR>\n" );
document.write( "cos = 3/sqrt(14)*sqrt(6)<BR>\n" );
document.write( "cos = 3/sqrt(84)<BR>\n" );
document.write( "angle = 70.89 degs\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );