document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=346160>Question 346160</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A) Find the inner product of a and b if a = <4, 5/4, -1/3> and b = < 1/2, -2, -3/2>, and state whether the vector are perpendicular.<BR>\n" );
document.write( "a. 5; no<BR>\n" );
document.write( "b. 5; yes<BR>\n" );
document.write( "c. 0; yes<BR>\n" );
document.write( "d. 0; no\r<BR>\n" );
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document.write( "B) Find the cross product of v and w if v = <-1/3, 4, -3/8> and w = < 6, -4/5, 4> </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #247681 by </B><A HREF=/tutors/aboutme.mpl?userid=nyc_function><B>nyc_function(2741)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nyc_function><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=nyc_function><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=247681\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please, post one question at a time.  I will answer part (a).\r<BR>\n" );
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document.write( "Let's compute the inner product, since that will maybe help with deciding which answer to pick.\r<BR>\n" );
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document.write( "a•b = 4(1/2) + (5/4)(-2) + (-1/3)(-3/2)\r<BR>\n" );
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document.write( "= 2 - 5/2 + 3/2\r<BR>\n" );
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document.write( "= 0\r<BR>\n" );
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document.write( "Then that narrows it down to (c) or (d).\r<BR>\n" );
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document.write( "Two vectors are perpendicular when their dot product is the cosine of 90 degrees, which is, as you may recall, 0.\r<BR>\n" );
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document.write( "Then (c) the correct answer.\r<BR>\n" );
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document.write( "============================\r<BR>\n" );
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document.write( "I decided to help you with question (b) as well.\r<BR>\n" );
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document.write( "Here we have\r<BR>\n" );
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document.write( "v = -i/3, 4j, -3k/8\r<BR>\n" );
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document.write( "w = 6i, -4j/5, 4k\r<BR>\n" );
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document.write( "v x w = (-i/3, 4j, -3k/8) x (6i, -4j/5, 4k)\r<BR>\n" );
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document.write( "v x w = 0 +4k/5 +4j/3 -24k +0 +16i -18j -12i/40 +0\r<BR>\n" );
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document.write( "v x w = (16 -12/40).i +(4/3 -18).j +(4/5 -24).k\r<BR>\n" );
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document.write( "v x w = 15.7(i) -50(j)/3 -116(k)/5 >================< ANSWER\r<BR>\n" );
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document.write( " </SPAN>\n" );
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