#!/usr/bin/env python3

# https://www.youtube.com/watch?v=L68VR5VuwnI&t=1h6m15s
# https://guide.handmadehero.org/code/day376/#3975

from sympy import *

vec = lambda v: [Symbol(f'{v}_{i}') for i in range(1, 3+1)]
dot = lambda a, b: sum(a_i * b_i for a_i, b_i in zip(a, b))

a = vec('a')
b = vec('b')
c = vec('c')

eqs = [
    Eq(dot(a, c), 0),
    Eq(dot(b, c), 0),
    Eq(dot(c, c), dot(a, a) * dot(b, b) - dot(a, b) * dot(a, b)),
]

sols = solve(eqs, *c, dict=True)
for sol in sols:
    pprint(sol)