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Math Help - 3D vector projection

  1. #1
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    3D vector projection

    Dear people,

    I need to calculate the projection of a 3D vector, but I don't know how. Could you please help me?

    There are two 3D vectors: A and B.

    A and B are both on plane P.

    L is a line on P, through the origin, and perpendicular to A.

    How do I calculate the vector C which is the projection of B on L?

    Thank you for your time!

    Cornelis
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  2. #2
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    Quote Originally Posted by feastures View Post
    Dear people,

    I need to calculate the projection of a 3D vector, but I don't know how. Could you please help me?

    There are two 3D vectors: A and B.

    A and B are both on plane P.

    L is a line on P, through the origin, and perpendicular to A.

    How do I calculate the vector C which is the projection of B on L?

    Thank you for your time!

    Cornelis
    C=proj_L B=\frac{<\mathbf{B},\mathbf{L}>}{||\mathbf{L}||}\m  athbf{L}
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  3. #3
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    Pretty sure this is 2nd or 3rd year calculus, not pre algebra.
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  4. #4
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    Thank!

    I'm not familiar with these notations so could you please explain how this works? Also, this definition can't be complete because A is not used.

    I need to write software that implements this, so I'm looking for a means of calculating this.
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  5. #5
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    Quote Originally Posted by feastures View Post
    Thank!

    I'm not familiar with these notations so could you please explain how this works? Also, this definition can't be complete because A is not used.

    I need to write software that implements this, so I'm looking for a means of calculating this.
    L=A\times B
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  6. #6
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    < , > inner product

    ||\ || norm
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  7. #7
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    Wow, thanks for the quick replies!

    Looking at my post, I want to apologize: Because I was too focussed on my problem, I forgot to mention that only A and B are known and that I need to calculate C (using P and L as possible intermediates). So you initial reply was complete.

    I will proceed to work this out.
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  8. #8
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    Quote Originally Posted by dwsmith View Post
    C=proj_L B=\frac{<\mathbf{B},\mathbf{L}>}{||\mathbf{L}||}\m  athbf{L}
    Wait a minute: L = AxB is perpendicular to both A and B. This is not what I want: A and B must be both on plane P. L must only be perpendicular to A, and L must be on P. So C will also be on P.

    Am I missing something?
    Last edited by feastures; May 19th 2010 at 12:02 AM.
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  9. #9
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    Quote Originally Posted by feastures View Post
    Wait a minute: L = AxB is perpendicular to both A and B. This is not what I want: A and B must be both on plane P. L must only be perpendicular to A, and L must be on P. So C will also be on P.

    Am I missing something?
    If two vectors are in the same plane, then a vector parallel to one will be parallel to the other. By taking the cross product of A and B, you will obtain your normal vector.
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