Two vectors `vecA` and `vecB` are such that `vecA+vecB=vecA-vecB`. Then

Options

A. `vec(A)*vec(B).=0`
B. `vec(A)xxvec(B)=0
C. `vec(a).vec(b)=vec(b).vec(c)=vec(c).vec(a)`
D. `vec(a)xxvec(b)+vec(b)xxvec(c)+vec(c)xxvec(a)=vec(0)`

Explanation

To solve the problem, we start with the equation given in the question:

### Step 1: Write down the given equation
We have:
\[ \vec{A} + \vec{B} = \vec{A} - \vec{B} \]

### Step 2: Rearrange the equation
To isolate the vectors, we can rearrange the equation:
\[ \vec{A} + \vec{B} - \vec{A} + \vec{B} = 0 \]
This simplifies to:
\[ 2\vec{B} = 0 \]

### Step 3: Solve for vector B
Dividing both sides by 2 gives us:
\[ \vec{B} = 0 \]
This means that vector \(\vec{B}\) is the null vector.

### Step 4: Analyze the implications
Since \(\vec{B} = 0\), we can analyze the implications for the dot and cross products:

1. **Cross Product**:
\[ \vec{A} \times \vec{B} = |\vec{A}| |\vec{B}| \sin \theta \]
Since \(|\vec{B}| = 0\), it follows that:
\[ \vec{A} \times \vec{B} = 0 \]

2. **Dot Product**:
\[ \vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos \theta \]
Again, since \(|\vec{B}| = 0\), we have:
\[ \vec{A} \cdot \vec{B} = 0 \]

### Step 5: Conclusion
From our analysis, we conclude:
- \(\vec{B} = 0\) (the null vector)
- \(\vec{A} \times \vec{B} = 0\)
- \(\vec{A} \cdot \vec{B} = 0\)

However, we cannot conclude anything about \(\vec{A}\) from the information given.

### Final Answer
The correct options based on the analysis are:
- \(\vec{A} \times \vec{B} = 0\)
- \(\vec{A} \cdot \vec{B} = 0\)
- \(\vec{B} = 0\)