TI-84 Plus CE and TI-83 Premium CE: Vectors Program
The program VECTORS is made for the TI-84 Plus CE and TI-83 Premium CE.
Introduction
The program VECTORS calculates the following of the three dimensional vectors [A] and [B]:
* Dot product of [A] and [B]
* Euclidean norm of vectors [A] and [B]
* Angle between vectors [A] and [B] in degrees
* Cross product of [A] × [B]
* Tensor product of [A] ⊗ [B]
The program uses the system matrices [A] and [B] and formats them as 3 rows, 1 column matrices. The program changes the angle mode to Degrees.
After entering each vector, the program gives you an option to normalize the vectors. Since the cross and tensor products do not follow the commutative property, there is an option to switch the elements of both vectors.
Depending on the calculator used, results will be shown in either exact format (TI-83 Premium CE) or approximate format (TI-84 CE).
Calculations Used
In this section, each of the vectors will be followed by the program code used.
Let [A] and [B] be the column vectors:
[A] = [[a1][a2][a3]]
[B] = [[b1][b2][b3]]
Dot Product:
[A] • [B] = a1 * b1 + a2 * b2 + a3 * b3 = [A]ᵀ [B]
Euclidean Norm:
||[A]||₂ = √(a1² + a2² + a3²) = √([A]ᵀ [A])
||[B]||₂ = √(b1² + b2² + b3²) = √([B]ᵀ [B])
Angle Between Two Vectors:
θ = arccos(([A] • [B]) ÷ (||[A]||₂ * ||[B]||₂))
Cross Product:
[A] × [B] = [C] where:
c1 = a2 * b3 – a3 * b2
c2 = -a1 * b3 + a3 * b1
c3 = a1 * b2 – a2 * b1
The result is a 3 x 1 matrix.
Tensor Product:
[A] ⊗ [B] = [A] [B]ᵀ
The result is a 3 x 3 matrix.
Download
You can download the program and the user guide here:
https://drive.google.com/file/d/1R1sHGfr8dKQDkH87QDE0HgMDWxeLNHPN/view?usp=share_link
Eddie
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