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defvector_sub(a,b):returnlist(map(lambdax,y:x-y,a,b))defcross(a,b):return[a[1]*b[2]-a[2]*b[1],a[2]*b[0]-a[0]*b[2],a[0]*b[1]-a[1]*b[0]]defdot(a,b):returnsum([x*yforx,yinzip(a,b)])defsolve(points):# use the 4 points p,q,r,s to make vectors pq,pr,ps pq=vector_sub(points[1],points[0])pr=vector_sub(points[2],points[0])ps=vector_sub(points[3],points[0])#crossproductofpqandprgivesthenormalvectorn=cross(pq,pr)# if the vector ps is orthoginal to n # then the point lies on the planeifdot(n,ps)!=0:return'NO'return'YES'
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Sherlock and Planes
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python3