what is the angle between `(overset(rarr)P+overset(rarr)Q)` and `(overset(rarr)P+overset(rarr)Q)`?

Options

A. 0
B. `(pi)/(2)`
C. `(pi)/(2)`
D. `pi`

Explanation

To find the angle between the vector sum of \(\vec{P} + \vec{Q}\) and itself, we can follow these steps:

### Step 1: Define the vectors
Let \(\vec{R} = \vec{P} + \vec{Q}\).

### Step 2: Identify the vectors in question
We need to find the angle between \(\vec{R}\) and \(\vec{R}\).

### Step 3: Understand the relationship between the vectors
Since both vectors are the same (\(\vec{R}\) and \(\vec{R}\)), they are parallel to each other.

### Step 4: Determine the angle between parallel vectors
The angle between any vector and itself is always \(0^\circ\) because they point in the same direction.

### Step 5: Conclusion
Therefore, the angle between \(\vec{R}\) and \(\vec{R}\) is \(0^\circ\).

### Final Answer:
The angle between \((\vec{P} + \vec{Q})\) and \((\vec{P} + \vec{Q})\) is \(0^\circ\).

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