document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147049>Question 147049</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find K so that the vectors [4,-3] and [k,-6] (a) point in the same direction<BR>\n" );
document.write( "(b) are perpendicular  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107395 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=107395\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)Point in the same direction means the vectors are scaled versions of each other. <BR>\n" );
document.write( "In other words, the x components are in the same proportion as the y components.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fk=%28-3%29%2F%28-6%29 ALIGN=MIDDLE  ALT=\"4%2Fk=%28-3%29%2F%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=8 ALIGN=MIDDLE  ALT=\"k=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b)Perpendicular vectors have a dot product equal to zero. <BR>\n" );
document.write( "A:[4,-3]<BR>\n" );
document.write( "B:[k,-6]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2AB=4%2Ak%2B%28-3%29%28-6%29=0 ALIGN=MIDDLE  ALT=\"A%2AB=4%2Ak%2B%28-3%29%28-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ak%2B18=0 ALIGN=MIDDLE  ALT=\"4%2Ak%2B18=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ak=-18 ALIGN=MIDDLE  ALT=\"4%2Ak=-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-18%2F4 ALIGN=MIDDLE  ALT=\"k=-18%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-9%2F2 ALIGN=MIDDLE  ALT=\"k=-9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-6%2C+6%2C+-6%2C+6%2Cgrid%28+1+%29%2Cblue%28line%280%2C0%2C-4.5%2C-6%29%29%2Cgreen%28line%28+0%2C0%2C+4%2C+-3%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Graphical check of the answer. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );