SOLUTION: 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

SOLUTION: 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

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.
Steps and notes on how to solve would be very helpful.
Thanks, -nick
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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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4x + y - z = 3
Its normal vector, A, is 4i + j - k
r = sqrt(16+1+1) = 3sqrt(2)
--------
2x - 5y + 3z =2
Its normal vector, B, is 2i - 5j + 3k
r = sqrt(4+25+9) = sqrt(38)
-------------------
Finding the angle between them will clarify it.
A dot B = |A||B|cos
A dot B = 8-5-3 = 0
Since the magnitudes of both A and B are non-zero, the cos = 0.
--> 90� orthogonal

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