if `vecP +vecQ = vecP -vecQ `, then

Options

A. `vecP = vec0`
B. `vecQ =vec0`
C. `|vecP|=1`
D. `|vecQ|=1`

Answer

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

### Step 1: Write down the given equation
We start with the equation:
\[ \vec{P} + \vec{Q} = \vec{P} - \vec{Q} \]

### Step 2: Subtract \( \vec{P} \) from both sides
To isolate the terms involving \( \vec{Q} \), we subtract \( \vec{P} \) from both sides:
\[ \vec{Q} = -\vec{Q} \]

### Step 3: Add \( \vec{Q} \) to both sides
Next, we add \( \vec{Q} \) to both sides to combine like terms:
\[ \vec{Q} + \vec{Q} = 0 \]
This simplifies to:
\[ 2\vec{Q} = 0 \]

### Step 4: Solve for \( \vec{Q} \)
Now, we divide both sides by 2:
\[ \vec{Q} = 0 \]

### Conclusion
Thus, we find that:
\[ \vec{Q} = 0 \]

### Step 5: Identify the correct option
Looking at the options provided, we see that option 2 states that \( \vec{Q} = 0 \), which is correct.