Produto Escalar: Comprimento e ângulos

• Produto Escalar: \(\underline{v} \cdot \underline{w}= \sum_{i=1}^n v_i w_i\)

  Python Listing: ../Vector.py. def Vector_Dot(v,w): if ( len(v)!=len(w) ): print "Vectors_Dot: Vectors does not have same length"; exit(); dot=0.0 for i in range( len(v) ): dot+=v[i]*w[i] return dot

• Comprimento: \(|\underline{v}|^2= \underline{v} \cdot \underline{v}\)

  Python Listing: ../Vector.py. def Vector_SqLen(v): return Vector_Dot(v,v) def Vector_Len(v): return sqrt( Vector_SqLen(v) )

• Ângulo: \(\displaystyle \cos{\theta}=\frac{ \underline{v} \cdot \underline{w} }{ |\underline{v}|~|\underline{w}| } \)

  Python Listing: ../Vector.py. def Vectors_Angle(v,w): return Vector_Dot(v,w)/( Vector_Len(v)*Vector_Len(w) )

• Normalização: \(\underline{e}=\frac{ \underline{v} }{ |\underline{v}| }\)

  Python Listing: ../Vector.py. def Vector_Normalize(v): length=Vector_Len(v) e=list(v) if (length>0.0): e=Vector_Mul( v,1.0/length ) return e