Two vectors `vec A and vec B` are such that `vec A + vec B = vec A- vec B`, then

Options

A. `vec A xx vec B=0`
B. `vec A cdot vec B=0`
C. `vec A =0`
D. `vec B =0`

Explanation

To solve the problem where two vectors \(\vec{A}\) and \(\vec{B}\) satisfy the equation \(\vec{A} + \vec{B} = \vec{A} - \vec{B}\), we can follow these steps:

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

### Step 2: Rearrange the equation
To isolate \(\vec{B}\), we can subtract \(\vec{A}\) from both sides:
\[ \vec{B} = \vec{A} - \vec{A} - \vec{B} \]
This simplifies to:
\[ \vec{B} + \vec{B} = 0 \]

### Step 3: Combine like terms
This can be rewritten as:
\[ 2\vec{B} = 0 \]

### Step 4: Solve for \(\vec{B}\)
Dividing both sides by 2 gives:
\[ \vec{B} = \vec{0} \]
This means that \(\vec{B}\) is the zero vector.

### Step 5: Conclusion
Since \(\vec{B} = \vec{0}\), we can conclude that the only solution for the given equation is that \(\vec{B}\) must be the zero vector.

### Final Statement
Thus, the answer to the question is that \(\vec{B}\) is the zero vector.

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