document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=665255>Question 665255</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me with this i really don't know how to do vectors, i have tried part a but i dont know if its right. <BR>\n" );
document.write( "Consider the two vectors a = î + &#309; and b = 2î – &#309; .<BR>\n" );
document.write( "(a) Calculate a + b and a – b .<BR>\n" );
document.write( "a + b = 2 î^2 + &#309;^2<BR>\n" );
document.write( "a – b = 2 <BR>\n" );
document.write( "(b) On a Cartesian plane, illustrate the vector addition a + b and the vector subtraction a – b. Clearly label your diagrams with all its appropriate vectors. <BR>\n" );
document.write( "(c) Calculate the magnitude of a and the magnitude of b. <BR>\n" );
document.write( "(d) Find the scalar product a•b. <BR>\n" );
document.write( "(e) Find the orthogonal projection of vector a onto vector b. That is, find the vector projb a . </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #413732 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=413732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider the two vectors a = i + j and b = 2i - j<BR>\n" );
document.write( "(a) Calculate a + b and a – b<BR>\n" );
document.write( "a + b:<BR>\n" );
document.write( "2 + 1 = 3<BR>\n" );
document.write( "1 - 1 = 0<BR>\n" );
document.write( "--> 3i<BR>\n" );
document.write( "==========================<BR>\n" );
document.write( "a – b:<BR>\n" );
document.write( "1 - 2 = -1<BR>\n" );
document.write( "1 - (-1) = 2<BR>\n" );
document.write( "--> -i + 2j<BR>\n" );
document.write( "================<BR>\n" );
document.write( "(b) On a Cartesian plane, illustrate the vector addition a + b and the vector subtraction a – b. Clearly label your diagrams with all its appropriate vectors. <BR>\n" );
document.write( "(c) Calculate the magnitude of a and the magnitude of b<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Mag+=+sqrt%28i%5E2+%2B+j%5E2%29 ALIGN=MIDDLE  ALT=\"Mag+=+sqrt%28i%5E2+%2B+j%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Mag+=+sqrt%281+%2B+1%29+=+sqrt%282%29 ALIGN=MIDDLE  ALT=\"Mag+=+sqrt%281+%2B+1%29+=+sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Mag+=+sqrt%285+%2B+1%29+=+sqrt%285%29 ALIGN=MIDDLE  ALT=\"Mag+=+sqrt%285+%2B+1%29+=+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "(d) Find the scalar product a•b<BR>\n" );
document.write( "a•b = 1*2 + 1*-1 = 1<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "(e) Find the orthogonal projection of vector a onto vector b. That is, find the vector projb a<BR>\n" );
document.write( "That's the dot product, = 1<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );