Given that `veca + vecb = veca-vecb`,. This can be true when

Options

A. `veca = vec0`
B. `vecb = vec0`
C. `veca and vecb` are parallel
D. `veca and vecb` are perpendicular

Answer

To solve the equation \( \vec{a} + \vec{b} = \vec{a} - \vec{b} \), we can follow these steps:

### Step 1: Rearrange the equation
Start by rearranging the given equation to isolate the terms involving \( \vec{b} \).

\[ \vec{a} + \vec{b} = \vec{a} - \vec{b} \]

Subtract \( \vec{a} \) from both sides:

\[ \vec{b} = -\vec{b} \]

### Step 2: Simplify the equation
Now, add \( \vec{b} \) to both sides of the equation:

\[ \vec{b} + \vec{b} = 0 \]

This simplifies to:

\[ 2\vec{b} = 0 \]

### Step 3: Solve for \( \vec{b} \)
Now, divide both sides by 2:

\[ \vec{b} = 0 \]

### Conclusion
The only condition under which the original equation holds true is when \( \vec{b} \) is equal to the zero vector.

Thus, the answer is that \( \vec{b} = 0 \).

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