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# SIgn command with dot products and vectors

Anonymous User
Anonymous User
Posted 10 years ago
 How would you use the sign command with the dot product to determine whether an angle between a pair of vectors is acute right or obtuse
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Posted 10 years ago
 Use A dot B = |A| |B| Cos(theta) where theta is the included angle.
Posted 10 years ago
 On uses the right hand rule: the first vector goes to the thumb, the second vector goes to the index finger, then the cross product is given perpendicular to the both as the middle finger. If one changes the sequence of the vectors, the middle finger directs to the reverse direction - move your hand, do not crash joints.The dot product and the VectorAngle do not mark the sequence of input vectors In[41]:= VectorAngle[ {2, -1, 1}, {3, 2, 1}] == VectorAngle[ {3, 2, 1}, {2, -1, 1}] Out[41]= True In[42]:= Dot[ {2, -1, 1}, {3, 2, 1}] == Dot[ {3, 2, 1}, {2, -1, 1}] Out[42]= True the cross product does In[46]:= Sign[Cross[ {2, -1, 1}, {3, 2, 1}]] Out[46]= {-1, 1, 1} In[43]:= Sign[Cross[ {2, -1, 1}, {3, 2, 1}]] == -Sign[Cross[ {3, 2, 1}, {2, -1, 1}]] Out[43]= True note that there is no single sign of a vector, it really just the right hand rule.If you want to know, whether the angle is right, use VectorAngle In[49]:= VectorAngle[ {1, 2, 3}, {-2, 1, 0}] Out[49]= \[Pi]/2 that's a right angle.