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# Class 2 – Find the Torsional Angle Hacker Rank Solution – Queslers

## Problem : Class 2 – Find the Torsional Angle in Python – Hacker Rank Solution

You are given four points A, B, c and D in a 3-dimensional Cartesian coordinate system. You are required to print the angle between the plane made by the points A, B, C and B, C, D in degrees(not radians). Let the angle be PHI.
Cos(PHI) = (X*Y) / |X| |Y| where X = ABxBC and Y = BC x CD.Here, X.Y means the dot product of X and Y, and ABxBC means the cross product of vectors and . Also, AB = B – A.

#### Input Format :

One line of input containing the space separated floating number values of the X,Y and Z coordinates of a point.

#### Output Format :

Output the angle correct up to two decimal places.

#### Sample Input :

``````0 4 5
1 7 6
0 5 9
1 7 2
``````

#### Sample Output :

``8.19``

### Class 2 – Find the Torsional Angle Hacker Rank Solution in python 2

``````import math

class Point:
"""docstring for Point"""
def __init__(self, x, y, z):
# super(Point, self).__init__()
self.x = x
self.y = y
self.z = z

def minus(self, other):
return Point(self.x - other.x, self.y - other.y, self.z - other.z)

def cross(self, other):
return Point( self.y * other.z - self.z * other.y
, self.z * other.x - self.x * other.z
, self.x * other.y - self.y * other.x)

def dot(self, other):
return self.x * other.x + self.y * other.y + self.z * other.z

def abs(self):
return math.sqrt(self.x * self.x + self.y * self.y + self.z * self.z)

def str(self):
return "(" + str(self.x) + ", " + str(self.y) + ", " + str(self.z) + ")"

def get_Point():
lst = map(float, raw_input().strip().split())
return Point(lst, lst, lst)

a = get_Point()
b = get_Point()
c = get_Point()
d = get_Point()

ab = a.minus(b)
bc = b.minus(c)
cd = c.minus(d)

x = ab.cross(bc)
y = bc.cross(cd)

v = x.dot(y) / (x.abs() * y.abs())

print "%.2f" % (math.acos(v) / math.acos(0) * 90,)``````

### Class 2 – Find the Torsional Angle Hacker Rank Solution in python 3

``````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)
``````

### Class 2 – Find the Torsional Angle Hacker Rank Solution in pypy

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

def __sub__(self, other):
return Points(self.x-other.x, self.y-other.y, self.z-other.z)

def dot(self, other):
return (self.x*other.x)+ (self.y*other.y )+ (self.z*other.z)
def cross(self, other):
return Points( self.y*other.z - self.z*other.y,
self.z*other.x - self.x*other.z,
self.x*other.y - self.y*other.x
)
def absolute(self):
return pow((self.x ** 2 + self.y ** 2 + self.z ** 2), 0.5)``````

### Class 2 – Find the Torsional Angle Hacker Rank Solution in pypy 3

``````from math import acos, sqrt, degrees

class Vector:
def __init__(self, x=0, y=0, z=0):
self.x = x
self.y = y
self.z = z

def __sub__(self, other):
return Vector(self.x - other.x, self.y - other.y, self.z - other.z)

def __mul__(self, other):
return self.x * other.x + self.y * other.y + self.z * other.z

def __and__(self, other):
return Vector(self.y * other.z - other.y * self.z,
other.x * self.z - self.x * other.z,
self.x * other.y - other.x * self.y)

def __abs__(self):
return sqrt(self * self)

return Vector(*[float(x) for x in input().split()])

X = (B - A) & (C - B)
Y = (C - B) & (D - C)
phi = degrees(acos((X * Y)/(abs(X) * abs(Y))))
print('{:0.2f}'.format(phi))``````
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