document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=18656>Question 18656</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABCD is a sqaure. The midpoints of BC and CD are M and N respectively.<BR>\n" );
document.write( "a) Express vector AM and vector An as linear combinations of vector AB and vector AD.<BR>\n" );
document.write( "b) Express vector AB and vector AD as linear combinations of vector AM and vector AN. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #9052 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=9052\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ABCD is a sqaure. The midpoints of BC and CD are M and N respectively.<BR>\n" );
document.write( "a) Express vector AM and vector An as linear combinations of vector AB and vector AD.<BR>\n" );
document.write( "b) Express vector AB and vector AD as linear combinations of vector AM and vector AN.<BR>\n" );
document.write( "ABCD being a square we have vector AB= vector DC<BR>\n" );
document.write( "and vector AD=vector BC<BR>\n" );
document.write( "but M is the mid point of BC .so vector BM=vector BC/2=vector AD/2<BR>\n" );
document.write( "anfd N is the midpoint of CD.so vector NC=vector DC/2=vector AB/2<BR>\n" );
document.write( "taking triangle ABM..we have vector AB+vector BM=vector AM<BR>\n" );
document.write( " or...vector AM=vector AB+vector AD/2...............(1)<BR>\n" );
document.write( "similarly we have from the polygon ABCN..<BR>\n" );
document.write( "vector AB+vector BC+vector CN=vector AN <BR>\n" );
document.write( "vector AN=vector AB+vector AD-vector NC=vector AB+vector AD-vector AB/2..or<BR>\n" );
document.write( "vector AN=vector AB/2+vector AD..............(2)<BR>\n" );
document.write( "from 2*(2)-(1) we get ..2*vector AN-vector AM=(2-1/2)(vector AD)=(3/2)vector AD<BR>\n" );
document.write( "hence ...vector AD=(2/3)(2*vector AN-vector AM)..similarly by taking 2*(2)-(1),we can find AB in terms of AM and AN<BR>\n" );
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document.write( " How do the graphs of y=X+3 (in <BR>\n" );
document.write( "square root) compare the graph of y=x (insquare root) where x is greater <BR>\n" );
document.write( "or equal to 0. And can you also graph y=f(x)+5<BR>\n" );
document.write( "y=SQRT(x+3)...for every value of x we get 2 values for y ..one +ve and anpther -ve.further x cannot be less than -3 as it will lead to -ve number under square root which is imaginary.so the tabulation reads as follows.now you can plot the graph,i suppose.<BR>\n" );
document.write( "x.....0.......1......2......3......-1......-2......-3<BR>\n" );
document.write( "y.....3^0.5...2......5^0.5..6^0.5...2^0.5..1.......0<BR>\n" );
document.write( "y....-3^0.5..-2.....-5^0.5.-6^0.5..-2^0.5.-1.......0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-3%2C+5%2C+-5%2C+5%2C+%2B%28x%2B3%29%5E0.5%2C-%28x%2B3%29%5E0.5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-3%2C+5%2C+-5%2C+5%2C+%2B%28x%2B3%29%5E0.5%2C-%28x%2B3%29%5E0.5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "y=sqrtx<BR>\n" );
document.write( "x.....0.......1......2......3.......4<BR>\n" );
document.write( "y.....0.......1......2^0.5..3^0.5...2<BR>\n" );
document.write( "y.....0......-1.....-2^0.5.-3^0.5..-2\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-3%2C+5%2C+-5%2C+5%2C+%2B%28x%29%5E0.5%2C-%28x%29%5E0.5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-3%2C+5%2C+-5%2C+5%2C+%2B%28x%29%5E0.5%2C-%28x%29%5E0.5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "graph y=f(x)+5...WHAT IS f(x)???????cant do wiyhout that\r<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );