2020-수학-가형-홀수-29¶
문제¶
풀이¶
from sympy import *
x0,y0,z0 = symbols('x0 y0 z0')
p0 = Point(x0,y0,z0)
a = Point(3,-3,3)
b = Point(-2, 7,-2)
sols = solve((Eq(p0.dot(a),1), Eq(p0.dot(b),1), Eq(p0.dot(p0),1)),(x0,y0,z0));
sols
[(1/3 - sqrt(3)/3, 1/3, 1/3 + sqrt(3)/3),
(1/3 + sqrt(3)/3, 1/3, 1/3 - sqrt(3)/3)]
c = Point(sols[0])
d = Point(sols[1])
import numpy as np
volume = simplify(abs(np.cross(b-a,c-a).dot(d-a)))/6
volume
\[\displaystyle \frac{20 \sqrt{3}}{9}\]