document.write( "Question 205335: Hi all, I asked this question recently, but did not get a response. Hopefully someone can help me this time. I need to Determine whether the the two planes; 4x+y-z = 3 and 2x - 5y + 3z =2 are parallel, orthogonal, conincident or none of these.
\n" ); document.write( "Steps and notes on how to solve would be very helpful.
\n" ); document.write( "Thanks, -nick \n" ); document.write( "
Algebra.Com's Answer #156542 by Alan3354(69443)\"\" \"About 
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Determine whether the the two planes; 4x+y-z = 3 and 2x - 5y + 3z =2 are parallel, orthogonal, conincident or none of these.
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\n" ); document.write( "4x + y - z = 3
\n" ); document.write( "Its normal vector, A, is 4i + j - k
\n" ); document.write( "r = sqrt(16+1+1) = 3sqrt(2)
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\n" ); document.write( "2x - 5y + 3z =2
\n" ); document.write( "Its normal vector, B, is 2i - 5j + 3k
\n" ); document.write( "r = sqrt(4+25+9) = sqrt(38)
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\n" ); document.write( "Finding the angle between them will clarify it.
\n" ); document.write( "A dot B = |A||B|cos
\n" ); document.write( "A dot B = 8-5-3 = 0
\n" ); document.write( "Since the magnitudes of both A and B are non-zero, the cos = 0.
\n" ); document.write( "--> 90º orthogonal
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