**Class 2 - Find the Torsional Angle python**

### Problem Statement :

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=AB x BC and Y= BC x CD. Here, X.Y means the dot product of X and Y, and AB x BC means the cross product of vectors AB and BC. 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.

### Solution :

` ````
Solution in C :
import operator
import math
def cross(p1, p2):
return [p1[1]*p2[2]-p1[2]*p2[1], p1[2]*p2[0]-p1[0]*p2[2], p1[0]*p2[1]-p1[1]*p2[0]]
def dot(p1, p2):
return sum(map(operator.mul, p1, p2))
def subtract(a, b):
return list(map(operator.sub, a, b))
def length(a):
return math.sqrt(dot(a,a))
def parsePoint(str):
components = str.split()
return list(map(float, components))
A = parsePoint(input())
B = parsePoint(input())
C = parsePoint(input())
D = parsePoint(input())
AB = subtract(A,B)
BC = subtract(B,C)
CD = subtract(C,D)
X = cross(AB,BC)
Y = cross(BC,CD)
PHI = math.degrees(math.acos(dot(X,Y)/(length(X)*length(Y))))
print("{0:.2f}".format(PHI))
```

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