document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=867363>Question 867363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have no clue how to do these problems. Please help \r<BR>\n" );
document.write( "\n" );
document.write( "Find the expression.<BR>\n" );
document.write( "1.) u = (-3,-2), v = (-8, -11) Find u-v<BR>\n" );
document.write( "choices: a.) (-5,-19) b.) (-1,3) c.) (5,9) d.) (-11,-13)\r<BR>\n" );
document.write( "\n" );
document.write( "2.) w = (-1,3) and v = (0,1) Find ||-4w -v||<BR>\n" );
document.write( "choices: a.) 185  b.)sqrt 185  c.) sqrt 155  d.) 155\r<BR>\n" );
document.write( "\n" );
document.write( "3.) u = 4i - 6j and v = -5i - 21j; Find ||v-u||<BR>\n" );
document.write( "choices: a.) sqrt 34  b.) -2 sqrt 34  c.) 3 sqrt 35  d.) 3 sqrt 34\r<BR>\n" );
document.write( "\n" );
document.write( "4.) if v = 3i + j and w = -10i + j; Find ||v + w||<BR>\n" );
document.write( "choices: a.) sqrt 130  b.) 13  c.) sqrt 53  d.) sqrt 111\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #522975 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=522975\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the expression.<BR>\n" );
document.write( "1.) u = (-3,-2), v = (-8, -11) Find u-v<BR>\n" );
document.write( "choices: a.) (-5,-19) b.) (-1,3) c.) (5,9) d.) (-11,-13)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simply subtract the corresponding elements like so:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "u - v = (-3,-2) - (-8, -11)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "u - v = (-3-(-8),-2-(-11))\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "u - v = (-3+8,-2+11)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "u - v = <font color=\"red\">(5,9)</font> which is <font color=\"red\">choice C</font><BR>\n" );
document.write( "-----------------------------------------------------------------------<BR>\n" );
document.write( "2.) w = (-1,3) and v = (0,1) Find ||-4w -v||<BR>\n" );
document.write( "choices: a.) 185  b.)sqrt 185  c.) sqrt 155  d.) 155\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "First multiply everything in w by -4 to get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "w = (-1,3)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-4w = -4(-1,3)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-4w = (-4(-1),-4(3))\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-4w = (4,-12)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then subtract off v\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-4w - v = (4,-12) - (0,1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-4w - v = (4-0,-12-1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-4w - v = (4,-13)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Finally, find the length of this vector using the formula ||x|| = sqrt(a^2 + b^2) where x = (a,b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "||-4w - v|| = sqrt((4)^2 + (-13)^2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "||-4w - v|| = sqrt(16+169)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "||-4w - v|| = <font color=\"red\">sqrt(185)</font>  which is <font color=\"red\">choice B</font><BR>\n" );
document.write( "-----------------------------------------------------------------------<BR>\n" );
document.write( "3.) u = 4i - 6j and v = -5i - 21j; Find ||v-u||<BR>\n" );
document.write( "choices: a.) sqrt 34  b.) -2 sqrt 34  c.) 3 sqrt 35  d.) 3 sqrt 34\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "First compute v-u\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v-u = (-5i - 21j) - (4i - 6j)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v-u = -5i - 21j - 4i + 6j\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v-u = -9i - 15j\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then find the length of this vector\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "||v-u|| = sqrt((-9)^2+(-15)^2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "||v-u|| = sqrt(81+225)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "||v-u|| = sqrt(306)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "||v-u|| = sqrt(9*34)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "||v-u|| = sqrt(9)*sqrt(34)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "||v-u|| = <font color=\"red\">3*sqrt(34)</font>  which is <font color=\"red\">choice D</font><BR>\n" );
document.write( "-----------------------------------------------------------------------<BR>\n" );
document.write( "4.) if v = 3i + j and w = -10i + j; Find ||v + w||<BR>\n" );
document.write( "choices: a.) sqrt 130  b.) 13  c.) sqrt 53  d.) sqrt 111\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Start by adding vectors v and w\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v + w = (3i+j) + (-10i+j)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v + w = 3i+j-10i+j\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v + w = -7i+2j\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now compute the length\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "||v + w|| = sqrt(a^2 + b^2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "||v + w|| = sqrt((-7)^2 + (2)^2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "||v + w|| = sqrt(49+4)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "||v + w|| = <font color=\"red\">sqrt(53)</font>  which is <font color=\"red\">choice C</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );