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Math Help - intersection

  1. #1
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    intersection

    From the point drawn normals to the two planes and have the equations and . A plane containing the two normals. Determine the intersection, and . (ON-system.) ima answer the intersection

    how shall i take dot product on this one?
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  2. #2
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    Re: intersection

    Hey Petrus.

    If two planes intersect then they are equal to each other.

    Can you solve the linear system corresponding to the intersection?

    (Hint: for the third plane the normal of this plane will correspond to the cross product of the two other normal vectors).
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  3. #3
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    Re: intersection

    Sorry idk what to do on this problem.. I cant solve the equation
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  4. #4
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    Re: intersection

    Recall that a plane in three dimensions has the form ax + by + cz = d for some constants a,b,c,d.

    Now you just have to solve a linear system with three of these equations where you solve for x given the system Ax = b.
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  5. #5
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    Re: intersection

    Do u mean like
    Y=8+2z?
    wha i thought i need to find the third plane to solve the linear equation
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  6. #6
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    Re: intersection

    That is one equation of a plane where Y - 2z = 8 where a = 0, b = 1, c = -2 and d = 8 in this particular example.
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  7. #7
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    Re: intersection

    I serious dont understand this one, any tips what i should read to get this... Im clueless
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  8. #8
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    Re: intersection

    Quote Originally Posted by Petrus View Post
    From the point drawn normals to the two planes and have the equations and . A plane containing the two normals. Determine the intersection, and . (ON-system.) ima answer the intersection

    Actually I have not idea exactly what that says.
    I think it means that P is not on either plane: \Pi_1:N_1\cdot (R-Q)=0~\&~\Pi_2:N_2\cdot (R-S)=0.

    The plane \Pi : (N_1\times N_2)\cdot (R-P)=0 contains the P and the two normals

    If that is not what you are asking, try to clear it up please.
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  9. #9
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    Re: intersection

    From the plane P draw the normal to the both i1 and i2 that have the equation x-y+5z=2 and y-2z=8. A plane i3 got the both normal. Decide the intersection between i1,i2 and i3 ( on bas)
    Thats My translate sorry i hope u understand but the answer shall be
    111/14,47/7,-9/14
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  10. #10
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    Re: intersection

    Quote Originally Posted by Petrus View Post
    From the plane P draw the normal to the both i1 and i2 that have the equation x-y+5z=2 and y-2z=8. A plane i3 got the both normal. Decide the intersection between i1,i2 and i3 ( on bas)
    Thats My translate sorry i hope u understand but the answer shall be
    111/14,47/7,-9/14

    Again, if we understand each other, then solve
    \begin{gathered}  3x - 2y - z =  - 1 \hfill \\  x - 2y - z =  - 2 \hfill \\  y - 2z = 8 \hfill \\ \end{gathered}
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  11. #11
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    Re: intersection

    Yes
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  12. #12
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    Re: intersection

    Did you take Plato's advice and solve the linear system?

    If you need to check your work use a program like Octave to do so which is free and you can download GUI octave for the MATLAB style window.
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  13. #13
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    Re: intersection

    If i understand right then x =-3/2 then ima solve rest somehow ? Is that program big? I got a really cheap pc so and its alredy so slow
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  14. #14
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    Re: intersection

    Since this is a 3x3 system with Ax = b we know that x = A^(-1)b and there are many websites that do matrix multiplication and inverse calculations.

    Here is one of them:

    3x3 Inverse Matrix Calculator & Calculation

    3x3 Matrix Multiplication Calculator, 3x3 Matrices Calculation Formula
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