Casio fx-4000P: Orthonormal 2D Vector Test
Introduction
A set of vectors form an orthonormal basis if the vectors are mutually perpendicular and are of unit length.
Mutual perpendicular means the dot product of two different vectors in the space is 0:
v_i ∙ v_j = 0, i ≠ j
Unit length means that the norm of each vector is 1:
|v_i| = 1
For two 2D vectors [ A, B ] and [ C, D ], the two vectors form an orthonormal basis if:
A^2 + B^2 = 1
C^2 + D^2 = 1
A * D + B * C = 0
Casio fx-4000P Program: Orthonormal 2D Vector Test
Bytes: 84 steps
(line returns are included for readability)
"A":
?→A:
"B":
?→B:
"C":
?→C:
"D":
?→D:
A²+B²≠1⇒Goto 0:
C²+D²≠1⇒Goto 0:
AD+BC≠0⇒Goto 0:
"YES" ⊿
Goto 1:
Lbl 0:
"NO" ⊿
Lbl 1
Examples
Example 1:
[1, 0], [0, 1]
A = 1, B = 0, C = 0, D = 1
"NO" (1*1 - 0*0 = 1)
Example 2:
[1/√2, 1/√2], [1/√2, -1/√2]
A = 1/√2, B = 1/√2, C = 1/√2, D = -1/√2
"YES"
Source:
Rowland, Todd. "Orthonormal Basis." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/OrthonormalBasis.html
Last Accessed April 7, 2022
Eddie
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