Okay, so I have two planes which intersect at a right angle. I have their normal vectors (which have different lengths). They intersect and form a line. I now need to find the equations of these two planes which are at an angle of 45deg between the two other planes.

this is the information I have

I tried normalizing the vectors, but that gives me ugly values. Any other way around?

  • $\begingroup$ Welcome to math.SE!! Please use MathJax to render math correctly. $\endgroup$
    – manooooh
    Oct 31, 2018 at 16:01

1 Answer 1


If you have normal vectors with equal lenghts, then the angle you are looking for is the sum of those two vectors. (Diagonal of a rhombus in general) Your normal vectors don't have equal lenght, so normalize them (divide by the corresponding lenght) and then add. You started correctly.

  • 1
    $\begingroup$ thank you! I did it that way and it's all good now. I just dislike seeing square roots. $\endgroup$
    – T jey
    Oct 31, 2018 at 17:52
  • $\begingroup$ @Tjey Get used to it. $\endgroup$
    – amd
    Nov 1, 2018 at 3:54

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