If `P+Q=0`. Then which of the following is necessarily true?

Options

A. P=0
B. P=-Q
C. Q=0
D. P=Q

Explanation

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

**Step 1:** Write down the given equation.
- We are given that \( P + Q = 0 \).

**Step 2:** Rearrange the equation to express one vector in terms of the other.
- From the equation \( P + Q = 0 \), we can rearrange it to find \( P \):
\[ P = -Q \]

**Step 3:** Analyze the implications of the equation.
- The equation \( P = -Q \) indicates that vector \( P \) is equal in magnitude but opposite in direction to vector \( Q \). This means that the two vectors are equal in size but point in opposite directions.

**Step 4:** Evaluate the options provided in the question.
- **Option 1:** \( P = 0 \) - This is not necessarily true because \( P \) could be a non-zero vector that is equal in magnitude and opposite in direction to \( Q \).
- **Option 2:** \( P = -Q \) - This is true as we derived this from the equation.
- **Option 3:** \( Q = 0 \) - This is also not necessarily true for the same reason as option 1.
- **Option 4:** \( P = Q \) - This is incorrect because \( P \) and \( Q \) are in opposite directions.

**Step 5:** Conclude which option is necessarily true.
- The only option that is necessarily true is:
\[ P = -Q \]
Thus, the correct answer is **Option 2**.

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