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Math Help - How to find out of planes are perpendicular

  1. #1
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    How to find out if planes are perpendicular

    Determine if planes in each pair are parallel, perpendicular, or neither.
    \pi_{1}: 4x-5y+z-9=0
    \pi_{2}: 2x-9y+z-2=0
    This is what I did
    n1 :[4, -5, 1]
    n2:[2, -9, 1]

    Dot product of n1 and n2 is not zero, so it's neither?

    \pi_{1}: 5x-6y+2z-2=0
    \pi_{2}: 2x-5y+-20z-2=0
    This is what I did
    n1 :[5, -6, 2]
    n2:[2, -5, -20]

    Dot product of n1 and n2 is zero


    What does that mean, is it parallel or perpendicular?

    and how do you find out if it's parallel or perpendicular

    Thanks
    Last edited by supersaiyan; April 22nd 2009 at 01:04 PM.
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  2. #2
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    Quote Originally Posted by supersaiyan View Post
    Determine if planes in each pair are parallel, perpendicular, or neither.
    \pi_{1}: 4x-5y+z-9=0
    \pi_{2}: 2x-9y+z-2=0
    This is what I did
    n1 :[4, -5, 1]
    n2:[2, -9, 1]

    Dot product of n1 and n2 is not zero, so it's neither?

    \pi_{1}: 5x-6y+2z-2=0
    \pi_{2}: 2x-5y+-20z-2=0
    This is what I did
    n1 :[5, -6, 2]
    n2:[2, -5, -20]

    Dot product of n1 and n2 is zero


    What does that mean, is it parallel or perpendicular?

    and how do you find out if it's parallel or perpendicular

    Thanks

    Two planes are parallel if their normal vectors are parallel.

    i.e one is a multiple of the other

    Two planes are perpendicular if their normal vectors are perpendicular.

    remember two vectors are perpendicular if their dot product is 0.

    If neither of the above to hold they are neither.

    I hope this helps
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