DuckieDai Vector Dot Product and Angle Python Program

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geometry · MIT License

Overview

Calculate dot product, magnitudes, angle, and angle class for 2D or 3D vectors.

Usage

Inputs

Two 2D or 3D vectors with finite components

Outputs

Dot product, magnitudes, angle in degrees, and perpendicular/acute/obtuse classification

Units: Both vectors must use compatible component units.

Assumptions and limitations

Assumptions

Neither vector is the zero vector when calculating an angle.

Constraints

Components must remain between -1e100 and 1e100; zero-vector angles are undefined.

Known failures

A zero vector cannot produce a direction or angle.

Compatibility and review

Review status: Tested on a TI calculator
Tested on: TI-84 Plus CE Python; OS 5.8.3; Python App 5.8.3.0048; exact source owner-tested through TI Connect CE
What happened: Owner confirmed the supplied vector dot product angle program runs on the physical calculator.
Dependencies: math
Suggested calculator name: VECDOT — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Browser preview

Try a 2D vector angle

This browser preview calculates the dot product and angle for two 2D vectors. The TI program also supports 3D vectors.

Simulation boundary: This preview uses a reviewed browser adapter. It does not execute the downloaded Python and does not prove TI-Python or calculator compatibility.

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Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

"""DuckieDai Vector Angle for TI-84 Plus CE Python."""

from math import sqrt, acos, degrees


def duckiedai_intro(program_name, wait=True):
    """Show the reusable DuckieDai program opening."""
    title = program_name[:16]
    empty = 16 - len(title)
    left = empty // 2
    right = empty - left

    print("+----------------------+")
    print("|   " + " " * left + title + " " * right + "   |")
    print("|                      |")
    print("|       __             |")
    print("|   ___(o )>  quack!   |")
    print("|   \\ <_. )           |")
    print("|    `---'             |")
    print("|     by DuckieDai     |")
    print("+----------------------+")
    print("Loading...")

    if wait:
        input("Press enter to start ")
        print("\n" * 6)


def number(prompt):
    """Allow positive, negative, or zero values."""
    while True:
        try:
            value = float(input(prompt))

            if value > -1e100 and value < 1e100:
                return value

        except ValueError:
            pass

        print("Enter a valid number.")


def safe_acos(value):
    """Protect acos from floating-point rounding."""
    if value > 1:
        value = 1

    if value < -1:
        value = -1

    return acos(value)


def magnitude(x, y, z=0):
    """Return vector magnitude."""
    return sqrt(
        x ** 2 +
        y ** 2 +
        z ** 2
    )


def main():
    duckiedai_intro("VECTOR ANGLE")

    print("VECTOR DOT PRODUCT")
    print("& ANGLE")
    print()
    print("1. 2D vectors")
    print("2. 3D vectors")
    print()

    choice = input("Choose 1 or 2: ")

    print()

    # ==========================================
    # 2D VECTOR INPUT
    # ==========================================

    if choice == "1":

        print("VECTOR u")
        ux = number("ux: ")
        uy = number("uy: ")
        uz = 0

        print()
        print("VECTOR v")
        vx = number("vx: ")
        vy = number("vy: ")
        vz = 0

    # ==========================================
    # 3D VECTOR INPUT
    # ==========================================

    elif choice == "2":

        print("VECTOR u")
        ux = number("ux: ")
        uy = number("uy: ")
        uz = number("uz: ")

        print()
        print("VECTOR v")
        vx = number("vx: ")
        vy = number("vy: ")
        vz = number("vz: ")

    else:

        print("Invalid choice.")
        print()
        print("DuckieDai says: done!")
        return

    # ==========================================
    # VECTOR MAGNITUDES
    # ==========================================

    mag_u = magnitude(
        ux, uy, uz
    )

    mag_v = magnitude(
        vx, vy, vz
    )

    # Angle is undefined if either vector
    # has zero magnitude.

    if mag_u == 0 or mag_v == 0:

        print()
        print("ANGLE UNDEFINED")
        print()
        print("A zero vector has")
        print("no direction.")
        print()
        print("DuckieDai says: done!")
        return

    # ==========================================
    # DOT PRODUCT
    #
    # u dot v =
    # ux*vx + uy*vy + uz*vz
    # ==========================================

    dot = (
        ux * vx +
        uy * vy +
        uz * vz
    )

    # ==========================================
    # ANGLE
    #
    # cos(theta) =
    # dot / (|u|*|v|)
    # ==========================================

    cos_theta = (
        dot /
        (mag_u * mag_v)
    )

    theta = degrees(
        safe_acos(cos_theta)
    )

    # ==========================================
    # RESULTS
    # ==========================================

    print()
    print("Using:")
    print("u dot v /")
    print("(|u|*|v|)")
    print()

    print("DOT PRODUCT")
    print("u dot v =")
    print(str(dot))
    print()

    print("MAGNITUDES")
    print("|u| = " + str(mag_u))
    print("|v| = " + str(mag_v))
    print()

    print("cos(theta) =")
    print(str(cos_theta))
    print()

    print("ANGLE")
    print("theta =")
    print(str(theta))
    print("degrees")
    print()

    # ==========================================
    # CLASSIFY ANGLE
    # ==========================================

    tolerance = 0.0000001

    if abs(dot) < tolerance:

        print("Vectors are")
        print("PERPENDICULAR.")

    elif dot > 0:

        print("Angle is ACUTE.")

    else:

        print("Angle is OBTUSE.")

    print()
    print("DuckieDai says: done!")


# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

"""DuckieDai Vector Angle for TI-84 Plus CE Python."""
from math import sqrt, acos, degrees
def duckiedai_intro(program_name, wait=True):
"""Show the reusable DuckieDai program opening."""
title = program_name[:16]
empty = 16 - len(title)
left = empty // 2
right = empty - left
print("+----------------------+")
print("| " + " " * left + title + " " * right + " |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n" * 6)
def number(prompt):
"""Allow positive, negative, or zero values."""
while True:
try:
value = float(input(prompt))
if value > -1e100 and value < 1e100:
return value
except ValueError:
pass
print("Enter a valid number.")
def safe_acos(value):
"""Protect acos from floating-point rounding."""
if value > 1:
value = 1
if value < -1:
value = -1
return acos(value)
def magnitude(x, y, z=0):
"""Return vector magnitude."""
return sqrt(
x ** 2 +
y ** 2 +
z ** 2
)
def main():
duckiedai_intro("VECTOR ANGLE")
print("VECTOR DOT PRODUCT")
print("& ANGLE")
print()
print("1. 2D vectors")
print("2. 3D vectors")
print()
choice = input("Choose 1 or 2: ")
print()
# ==========================================
# 2D VECTOR INPUT
# ==========================================
if choice == "1":
print("VECTOR u")
ux = number("ux: ")
uy = number("uy: ")
uz = 0
print()
print("VECTOR v")
vx = number("vx: ")
vy = number("vy: ")
vz = 0
# ==========================================
# 3D VECTOR INPUT
# ==========================================
elif choice == "2":
print("VECTOR u")
ux = number("ux: ")
uy = number("uy: ")
uz = number("uz: ")
print()
print("VECTOR v")
vx = number("vx: ")
vy = number("vy: ")
vz = number("vz: ")
else:
print("Invalid choice.")
print()
print("DuckieDai says: done!")
return
# ==========================================
# VECTOR MAGNITUDES
# ==========================================
mag_u = magnitude(
ux, uy, uz
)
mag_v = magnitude(
vx, vy, vz
)
# Angle is undefined if either vector
# has zero magnitude.
if mag_u == 0 or mag_v == 0:
print()
print("ANGLE UNDEFINED")
print()
print("A zero vector has")
print("no direction.")
print()
print("DuckieDai says: done!")
return
# ==========================================
# DOT PRODUCT
#
# u dot v =
# ux*vx + uy*vy + uz*vz
# ==========================================
dot = (
ux * vx +
uy * vy +
uz * vz
)
# ==========================================
# ANGLE
#
# cos(theta) =
# dot / (|u|*|v|)
# ==========================================
cos_theta = (
dot /
(mag_u * mag_v)
)
theta = degrees(
safe_acos(cos_theta)
)
# ==========================================
# RESULTS
# ==========================================
print()
print("Using:")
print("u dot v /")
print("(|u|*|v|)")
print()
print("DOT PRODUCT")
print("u dot v =")
print(str(dot))
print()
print("MAGNITUDES")
print("|u| = " + str(mag_u))
print("|v| = " + str(mag_v))
print()
print("cos(theta) =")
print(str(cos_theta))
print()
print("ANGLE")
print("theta =")
print(str(theta))
print("degrees")
print()
# ==========================================
# CLASSIFY ANGLE
# ==========================================
tolerance = 0.0000001
if abs(dot) < tolerance:
print("Vectors are")
print("PERPENDICULAR.")
elif dot > 0:
print("Angle is ACUTE.")
else:
print("Angle is OBTUSE.")
print()
print("DuckieDai says: done!")
# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

Filename: VECDOT.py
Size: 4772 bytes
SHA-256: ce10c3625e3880468361fd5b292e2d982ecf2ee49a0fba89e9e6959eccb7dcc8

Transfer and launch

Confirm that your calculator is the Python-capable model named above. Check that its OS and Python App versions match the reviewed record.
Download the .py source above and verify its SHA-256 digest if your computer provides that option.
Use TI Connect CE to send the Python file to a compatible calculator. VECDOT is a suggested name; you may choose another valid, unique calculator name.
Open the Python App, select the program, and check sample inputs before relying on other results.

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Version history

1.0.0 — current version, published 2026-09-24. Download this reviewed version

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