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mathvectormath

Solve for a vector given one component and direction expressed as a unit vector

Say that I have the y-component of a 3D vector and I have a unit vector expressing the direction of the final desired vector. How would I go about solving for the X and Z components? Thanks!

Solution

  • Simple ratio, where u* are unit vector components

     dx = ux * dy / uy
 dz = uz * dy / uy

    (because unit vector components are defined as ux = dx / Len with common Len, and dy/uy is really vector length)