Vectors on 15c?



#4

I know the 15c did matrices but could it do vector math as well. Or did it have to be programed to do the cross product, spherical, and angle between vectors?


#5

Hi, Ron;

it may seem obvious, but if you are dealing with 2D vectors (plain), you can use some complex functions that will give equivalent NUMERICAL results. Just for the records: do you already use complex numbers in the HP15C?

If you are dealing with 3D vectors (as you mention spherical), I think some small programs would help.

What I am not sure is if some matrix operations could help if you consider [1×3] or [3×1] matrices as 3D vectors. I don't remember it well (it takes a long time since I needed it), but I think some matrix operations apply to 3D vectors and give numerical equivalent results as well. One of the contributors that has one of the deepest knowledge about the HP15C and applied math is Valentim. I know that others know it as well, but Valentim is always bringing some tricky challenges to this forum and his answers are quite clever and thoughtful.

For sure someone else will post something more. Sorry not helping that much.

Cheers.

Luiz (Brazil)

#6

Ron --

No, unfortunately, the HP-15C did not have specific vector-calculus functions built in, as did the HP-42S. However, one could use the built-in matrix functions for performing dot product and angle between vectors of any dimension within memory limits:

  1. Load vectors into two (n x 1) row-vector matrices.
  2. "A dot B" (e.g.) would be ATB -- use "MATRIX 5".
  3. Angle between A and B would be cos-1 of ("A dot B" over the product of magnitudes of A and B) -- use "MATRIX 8" (Frobenius norm) to get the magnitudes.

Vector cross product could be calculated using built-in determinant function ("MATRIX 9") three times, but it would be faster and more space-efficient to calculate it directly from stored vectors. Use "RCL g {A-E}" and "STO g {A-E}".

Coordinate conversion would be a programming task. I'd recommend getting a HP-48* for that. (HP-41C* with Math Pac would also work.)


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