Input Format
One line of input containing the space separated floating number values of the  and  coordinates of a point.
Output Format
Output the angle correct up to two decimal places.

hackerrank class 2 find the torsional angle problem solution in python

Problem solution in Python 3 programming language.

import math
class Points(object):
    def __init__(self, x, y, z):
        self.x=x
        self.y=y
        self.z=z
    def __sub__(self, no):
        return  Points((self.x-no.x),(self.y-no.y),(self.z-no.z))
    def dot(self, no):
        return (self.x*no.x)+(self.y*no.y)+(self.z*no.z)
    def cross(self, no):
        return Points((self.y*no.z-self.z*no.y),(self.z*no.x-self.x*no.z),
(self.x*no.y-self.y*no.x))

    def absolute(self):
        return pow((self.x ** 2 + self.y ** 2 + self.z ** 2), 0.5)
if __name__ == '__main__':
    points = list()
    for i in range(4):
        a = list(map(float, input().split()))
        points.append(a)
    a, b, c, d = Points(*points[0]), Points(*points[1]), 
Points(*points[2]), Points(*points[3])
    x = (b - a).cross(c - b)
    y = (c - b).cross(d - c)
    angle = math.acos(x.dot(y) / (x.absolute() * y.absolute())
    print("%.2f" % math.degrees(angle))

Problem solution in Python 2 programming language.

import math

class Points(object):
    def __init__(self, x, y, z):
        self.x = x
        self.y = y
        self.z = z

    def __sub__(self, no):
        x = self.x - no.x
        y = self.y - no.y
        z = self.z - no.z
        return Points(x, y, z)

    def dot(self, no):
        x = self.x * no.x
        y = self.y * no.y
        z = self.z * no.z
        return x + y + z

    def cross(self, no):
        x = self.y * no.z - self.z * no.y
        y = self.z * no.x - self.x * no.z
        z = self.x * no.y - self.y * no.x
        return Points(x, y, z)

    def absolute(self):
        return pow((self.x ** 2 + self.y ** 2 + self.z ** 2), 0.5)


points = list()
for i in range(4):
    a = map(float, raw_input().split())
    points.append(a)

A, B, C, D = Points(*points[0]), Points(*points[1]), Points(*points[2]), Points(*points[3])
X = (B - A).cross(C - B)
Y = (C - B).cross(D - C)
angle = math.acos(X.dot(Y) / (X.absolute() * Y.absolute()))

print "%.2f" % math.degrees(angle)