CODEWITHSUNDEEP
wolfram-mathematica
tiankonghewo
tiankonghewo

Reputation: 133

How to simplify the abstract vector operation in Mathematica?

for example, I have two vectors:

   a,b

I need to simplify the following simple equation :

|a+b|==|a-b|

We can know by artificial calculation:

 a.b==0

Now I tried the following expression in Mathematica:

In[1040]=
         Reduce[{a, b} \[Element] Vectors[2, Reals] && (a + b).(a + b) == (a - b).(a - b)]

but keep it as it is. 

Out[1040]=
        Reduce[(a | b) \[Element] Reals && (a + b).(a + b) == (a - b).(a - b)]

Upvotes: 0

Views: 398

Answers (1)

Kh40tiK
Kh40tiK

Reputation: 2336

With a little help with TensorReduce:

assumptions = Element[#, Vectors[2, Reals]] & /@ {a, b};
Reduce@TensorReduce[(a + b).(a + b) == (a - b).(a - b), Assumptions->assumptions]

Output:

a.b == 0

Upvotes: 1

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