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Math Help - Combining Vectors

  1. #1
    IMK
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    Combining Vectors

    Hello, was wondering if someone could help me with a little vector maths problem please.

    What I need to find is the angle between two vectors that are derived from/relative to a third vector.

    So what I having working/understood is that theta = cos-1(“vector a” * “vector b”) where “vector a” and “vector b” are 3d vectors at 90 deg to each other, x,y,z.
    Basically the cos of the dot product of the two vectors…

    What I now wish to do is to offset “vector a” and “vector b” by another vector, “vector c” and I have tried the following with mixed results.

    (1) “vector a” = “vector a” - “vector c”, “vector b” = “vector b” - “vector c”
    this returns an answer that is obviously incorrect.

    (2) “vector a”= sqrt( “vector a” * “vector c”), “vector b” = sqrt(“vector b” *“vector c”), this returns an answer that seems to be correct as I can swap around the x,y,z values any of the vectors and the result seem to be consistent.

    However I have no way of really proving the result, so can you help please?

    Many thanks in advance IMK

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  2. #2
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    Quote Originally Posted by IMK View Post
    Hello, was wondering if someone could help me with a little vector maths problem please.

    What I need to find is the angle between two vectors that are derived from/relative to a third vector.

    So what I having working/understood is that theta = cos-1(“vector a” * “vector b”) where “vector a” and “vector b” are 3d vectors at 90 deg to each other, x,y,z.
    Basically the cos of the dot product of the two vectors…

    What I now wish to do is to offset “vector a” and “vector b” by another vector, “vector c” and I have tried the following with mixed results.

    (1) “vector a” = “vector a” - “vector c”, “vector b” = “vector b” - “vector c”
    this returns an answer that is obviously incorrect.

    (2) “vector a”= sqrt( “vector a” * “vector c”), “vector b” = sqrt(“vector b” *“vector c”), this returns an answer that seems to be correct as I can swap around the x,y,z values any of the vectors and the result seem to be consistent.

    However I have no way of really proving the result, so can you help please?

    Many thanks in advance IMK
    You have two vectors, a and b. You wish to off-set them by a third vector c, and find the angle between the new vectors?

    Graph what you are doing. The vector a - c is not parallel to the vector a. Similarly b - c is not parallel to the vector b. What you want is to translate the coordinate axes by some amount. But when you do that you find that you have the same components for vectors a and b. (Remember that the coordinate form for a vector is the coordinates of the head minus the coordinates of the tail.)

    -Dan
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