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Math Help - Find a vector3 that is perpendicular to another vector3 and (0,1,0)?

  1. #1
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    Find a vector3 that is perpendicular to another vector3 and (0,1,0)?

    Hi everyone,
    recently I was trying to solve this problem:

    Find a vector3 that is perpendicular to another vector3 and (0,1,0)?-vectorquestion.png
    If I know 3D position vectors P0 and P1 how would I go about solving for P2 and P3?
    I assumed it would be by taking the cross product of the vector P1 - P0 with an arbitrary basis vector like (0,1,0)
    something like

    Vector3 perpendicularVector = Vector3.Cross((P1-P0), Vector3.Up);

    but I wasn't able to make that work.

    Any help on why my understanding is flawed and what I need to study to be able to understand a problem like this would be greatly appreciated!
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  2. #2
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    Re: Find a vector3 that is perpendicular to another vector3 and (0,1,0)?

    Quote Originally Posted by winterkewl View Post
    Hi everyone,
    recently I was trying to solve this problem:

    Click image for larger version. 

Name:	vectorQuestion.png 
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ID:	24268
    If I know 3D position vectors P0 and P1 how would I go about solving for P2 and P3?
    I assumed it would be by taking the cross product of the vector P1 - P0 with an arbitrary basis vector like (0,1,0)
    something like
    Vector3 perpendicularVector = Vector3.Cross((P1-P0), Vector3.Up);
    I don't really understand what is going on here.
    But \overrightarrow {{P_0}{P_1}}  = \left\langle {1,1,0} \right\rangle

    There is no unique answer to this \overrightarrow {{P_0}{P_2}}  = \left\langle {a,b,c} \right\rangle where a+b=0 and c can be any real.
    If that is true then \overrightarrow {{P_0}{P_1}}  \bot \overrightarrow {{P_0}{P_2}}.
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    Re: Find a vector3 that is perpendicular to another vector3 and (0,1,0)?

    Hi Plato,

    Thanks for your answer! I was pretty sure I was going about this problem the incorrect way...curse my art degree!

    Maybe I can clarify what I'm attempting and you can tell me the proper way to go about solving a problem like this.
    Say a user can draw a line by choosing a starting location on a 2d grid and an ending location on that same 2d grid.
    I'd like to have that action result in the pictured rectangle and not just the 2 points that the user provided.
    Does that make any more sense?

    of topic: If there is a text that would help me more accurately understand these types of problems that you can recommend I'd love any suggested readings!
    Thanks!
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    Re: Find a vector3 that is perpendicular to another vector3 and (0,1,0)?

    Quote Originally Posted by winterkewl View Post
    Say a user can draw a line by choosing a starting location on a 2d grid and an ending location on that same 2d grid.
    I'd like to have that action result in the pictured rectangle and not just the 2 points that the user provided.
    Does that make any more sense?
    Is it 2d grid or 3d grid? If it is a 2d grid, the why did you post 3d example?
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    Re: Find a vector3 that is perpendicular to another vector3 and (0,1,0)?

    I'm sorry,

    I constrained my "clarification example" to 2 dimensions because I thought it would make the explanation easier...
    The ultimate solution I was looking for would be in 3 dimensions.

    I want to find the corners of a cube with arbitrary length, width, and depth but I only have to 2 positions in 3D space, and the Basis vectors as input.

    If that problem is nonsensical (and the more I say it, it sure sounds like it) then I apologize for wasting your time, but appreciate the knowledge.
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  6. #6
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    Re: Find a vector3 that is perpendicular to another vector3 and (0,1,0)?

    Quote Originally Posted by winterkewl View Post
    I constrained my "clarification example" to 2 dimensions because I thought it would make the explanation easier... The ultimate solution I was looking for would be in 3 dimensions.
    I want to find the corners of a cube with arbitrary length, width, and depth but I only have to 2 positions in 3D space, and the Basis vectors as input. If that problem is nonsensical (and the more I say it, it sure sounds like it) then I apologize for wasting your time, but appreciate the knowledge.
    (0,0,0),~(1,0,0),~(1,1,0),~(0,1,0),~(0,1,1),~(0,0,  1),~(1,0,1),~(1,1.1) are the eight vertices of a unit cube.
    Its faces parallel to the principal planes.

    You need a good deal of mathematics to adjust the lengths of the sides, and to rotate the cube is 3d space.
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    Re: Find a vector3 that is perpendicular to another vector3 and (0,1,0)?

    Thanks yeah I got that far as well,
    made the cube at the origin with the arbitrary lengths then transformed that result to the position P0 and oriented to look at P2,
    I just feel like there is a major bit of Vector transformations and indeed Vector's themselves that I'm missing something fundamental here.
    Thanks for your help!
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