document.write( "Question 196181: Hi, Just wondering if anyone can help with the following question, im struggling a bit.
\n" ); document.write( "For the given vectors find: (a) scalar product and
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\n" ); document.write( "a = 2 i − j + 3 k ,
\n" ); document.write( "b = −i − 7j . \n" ); document.write( "
Algebra.Com's Answer #147061 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Italicized letters such as a represent vectors\r\n" );
document.write( "Regular letters represent scalars which are\r\n" );
document.write( "just plain old numbers.\r\n" );
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document.write( "The scalar product:\r\n" );
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document.write( "That's the kind of multiplying where you multiply\r\n" );
document.write( "two vectors and get a \"non-vector\", called a scalar,\r\n" );
document.write( "which is nothing but a PLAIN OLD NUMBER.\r\n" );
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document.write( "There are two separate formulas for the scalar product.\r\n" );
document.write( "You use whichever one you need depending on what you\r\n" );
document.write( "have given.\r\n" );
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document.write( "The first formula is the basic one:\r\n" );
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document.write( "a = mi + nj + pk \r\n" );
document.write( "b = qi + rj + sk\r\n" );
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document.write( "a·b = (mi + nj + pk)·(qi + rj + sk) = mq + nr + ps\r\n" );
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document.write( "so for\r\n" );
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document.write( "(2i - j + 3k)·(-i - 7j)\r\n" );
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document.write( "First we rewrite it to show the coefficients\r\n" );
document.write( "-1 on j in the first and i in the second, and \r\n" );
document.write( "put \"+ 0k\" as a placeholder for the k-component \r\n" );
document.write( "in the second one:\r\n" );
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document.write( "(2i - 1j + 3k)·(-1i - 7j + 0k)\r\n" );
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document.write( "m=2, n=-1, p=3, q=-1, r=-7, s=0\r\n" );
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document.write( "So\r\n" );
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document.write( "(mi + nj + pk)·(qi + rj + sk) = mq + nr + ps\r\n" );
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document.write( "becomes\r\n" );
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document.write( "[(2)i + (-1)j + (3)k]·[(-1)i + (-7)j + (0)i] =\r\n" );
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document.write( "(2)(-1) + (-1)(-7) + (3)(0) = -2 + 7 + 0 = 5.\r\n" );
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document.write( "So their scalar product (also called \"dot product\")\r\n" );
document.write( "is simply the scalar, (or plain old number), 5.\r\n" );
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document.write( "Now we look at the other formula for the scalar product:\r\n" );
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document.write( "a·b = |a||b|cosq where q is the angle between the \r\n" );
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document.write( "vectors a and b, and where |a| and |b| represent the\r\n" );
document.write( "scalar (plain old number) magnitude, which is just\r\n" );
document.write( "the length of the vector. It is found by the extended\r\n" );
document.write( "Pythagorean formula:\r\n" );
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document.write( "|a| = |mi + nj + pk| = \r\n" );
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document.write( "Ö(m2 + n2 + p2) \r\n" );
document.write( "|b| =\r\n" );
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document.write( "|qi + rj + sk| =\r\n" );
document.write( " ____________ \r\n" );
document.write( "Ö(q2 + r2 + s2)\r\n" );
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document.write( "So:\r\n" );
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document.write( "|a| = |2i - 1j + 3k| = \r\n" );
document.write( " ___________________\r\n" );
document.write( "Ö(2)2 + (-1)2 + (3)2 =\r\n" );
document.write( " _________\r\n" );
document.write( "Ö4 + 1 + 9 = \r\n" );
document.write( " __\r\n" );
document.write( "Ö14\r\n" );
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document.write( "and\r\n" );
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document.write( "|b| = |-1i - 7j + 0k| =\r\n" );
document.write( " ___________________\r\n" );
document.write( "Ö(-1)2 + (-7)2 + (0)2 =\r\n" );
document.write( " ____________\r\n" );
document.write( "Ö1 + (49) + 0 = \r\n" );
document.write( " __                                 \r\n" );
document.write( "Ö50 =\r\n" );
document.write( "  _______\r\n" );
document.write( "Ö(25)(2) = \r\n" );
document.write( "  _\r\n" );
document.write( "5Ö2\r\n" );
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document.write( "Substituting in \r\n" );
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document.write( "a·b = |a||b|cosq\r\n" );
document.write( "      __                                 _\r\n" );
document.write( "5 = (Ö14)(5Ö2)cosq\r\n" );
document.write( "      __\r\n" );
document.write( "5 = 5Ö28)cosq\r\n" );
document.write( "      ______\r\n" );
document.write( "5 = 5Ö(4)(7)*cosq\r\n" );
document.write( "         _\r\n" );
document.write( "5 = 5(2)Ö7*cosq\r\n" );
document.write( "       _                \r\n" );
document.write( "5 = 10Ö7*cosq\r\n" );
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document.write( "\"5%2F%2810sqrt%287%29%29\" = cosq\r\n" );
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document.write( "\"1%2F%282sqrt%287%29%29\" = cosq\r\n" );
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document.write( "Get the inverse cosine of \"1%2F%282sqrt%287%29%29\"\r\n" );
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document.write( "q = 79.10° approximately\r\n" );
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document.write( "Edwin

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