document.write( "Question 166636: Find c so that the vectors v = i + j and w = i + c j are orthogonal \n" ); document.write( "
Algebra.Com's Answer #122811 by jim_thompson5910(35256)\"\" \"About 
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The vectors are orthogonal if their dot product is 0. So in this case v=<1,1> and w=<1,c>\r
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\n" ); document.write( "\n" ); document.write( "Now take the dot product:\r
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\n" ); document.write( "\n" ); document.write( "v · w = 1*1+1*c = 1+c\r
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\n" ); document.write( "\n" ); document.write( "Now set the dot product equal to zero\r
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\n" ); document.write( "\n" ); document.write( "1+c=0\r
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\n" ); document.write( "\n" ); document.write( "Now solve for c\r
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\n" ); document.write( "\n" ); document.write( "c=-1\r
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\n" ); document.write( "\n" ); document.write( "So if c=-1, then the dot product will be zero. This means that if c=-1, then v and w are orthogonal\r
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\n" ); document.write( "\n" ); document.write( "If this is hard to grasp, draw a picture of the vectors and you'll see that the two vectors <1,1> and <1,-1> are orthogonal (perpendicular) \n" ); document.write( "
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