document.write( "Question 206412: Hi all, can anyone show me how to do the following? Show that the lines
\n" ); document.write( "[(x-2)/5] = [y+3/-3] = [(z-5)/2] and [(x-3)/4 = [(y-2)/6] = [(z-10)/1]
\n" ); document.write( "are orthagonal.
\n" ); document.write( "Would be very hwlpful,
\n" ); document.write( "Thnaks, -nick.
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Algebra.Com's Answer #155978 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
I did this one yesterday.\r
\n" ); document.write( "\n" ); document.write( "Answer 155851 by Alan3354(4187) on 2009-08-11 14:06:22 (Show Source): \r
\n" ); document.write( "\n" ); document.write( "You can put this solution on YOUR website!
\n" ); document.write( "I need to show that the lines:
\n" ); document.write( "[(x-2)/5] = [(y+3)/-3] = [(x-5)/2] and [(x-3)/4] = [(y-2)/6] = [(z-10)/-1] are orthagonal.
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\n" ); document.write( "(x-2)/5 = (y+3)/-3 = (x-5)/2 (I think the last term is z)
\n" ); document.write( "x = 5t+2, y = -3t-3, z = 2t+5
\n" ); document.write( "Direction vector v1 = (5,-3,2)
\n" ); document.write( "ABS(v1) = sqrt(25 + 9 + 4) = sqrt(38)
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\n" ); document.write( "(x-3)/4 = (y-2)/6 = (z-10)/-1
\n" ); document.write( "Direction vector v2 = (4,6,-1)
\n" ); document.write( "ABS(v2) = sqrt(16+36+1) = sqrt(53)
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\n" ); document.write( "v1 dot v2 = (5*4 + -3*6 + 2*-1) = 0
\n" ); document.write( "Since the lengths (ABS) are not zero, the cosine of the angle between is zero.
\n" ); document.write( "So the angle between the vectors (and the 2 lines) is 90 degrees.
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