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Math Help - Angles between planes

  1. #1
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    Angles between planes

    I need to find the angle between the planes x-z=1 and 2y+z=1

    So the normal vectors for the planes would be
    <1,0,-1) and <0,2,1) Correct?

    And the magnitudes of those vectors would be
    (2)^(1/2) and (5)^(1/2) Correct?

    Thus Cos(Theta)= -1/((2^.5)*(5^.5))
    Correct?

    Leaving me with an angle of 1.8925 Radians?

    Is this all correct?
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  2. #2
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    Re: Angles between planes

    Looks good to me, though I've been having trouble since my hari-kari.
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  3. #3
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    Re: Angles between planes

    Well, this is the wrong answer...unless the teacher is wrong. So I'm trying to figure out what's wrong here.
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    Re: Angles between planes

    Quote Originally Posted by Bracketology View Post
    Well, this is the wrong answer...unless the teacher is wrong. So I'm trying to figure out what's wrong here.
    Is your teacher's answer 1.249~?
    That is the acute angle between the plane,
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    Re: Angles between planes

    Yes. How do I find this angle?
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    Re: Angles between planes

    Quote Originally Posted by Bracketology View Post
    Yes. How do I find this angle?
    It usual in such a question to find the acute angle or maybe right angle.
    \Theta  = \arccos \left( {\frac{{\left| {u \cdot v} \right|}}{{\left\| u \right\| \cdot \left\| v \right\|}}} \right)~.
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    Re: Angles between planes

    Quote Originally Posted by Bracketology View Post
    Yes. How do I find this angle?
    Pi - 1.89 (!)
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  8. #8
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    Re: Angles between planes

    When two planes (or two lines) intersect they make four angles but only two distinct angles- the "opposite" (vertical) angles are congruent. The two distinct angles between two planes add to \pi radians. \pi- 1.8925=1.2491 radians.

    As to why that formula did not immediately give you the correct answer, note that <-1, 0, 1> is also normal to the first plane and if you had used that, you would have got cos(\theta)= \frac{1}{\sqrt{2}\sqrt{5}}. I.e., to get the smaller angle, use the absolute value.
    Last edited by Ackbeet; September 14th 2011 at 03:55 PM.
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  9. #9
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    Re: Angles between planes

    Thanks for all the help guys!
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