If `vecA+ vecB = vecC and A+B+C=0`, then the angle between `vecA and vecB` is :

Options

A. 0
B. `(pi)/(4)`
C. `(pi)/(2)`
D. `pi`

Explanation

To solve the problem, we need to find the angle between vectors \(\vec{A}\) and \(\vec{B}\) given the conditions:

1. \(\vec{A} + \vec{B} = \vec{C}\)
2. \(\vec{A} + \vec{B} + \vec{C} = 0\)

### Step 1: Understand the implications of the equations

From the second equation, \(\vec{A} + \vec{B} + \vec{C} = 0\), we can rearrange it to find:

\[ \vec{C} = -(\vec{A} + \vec{B}) \]

### Step 2: Substitute \(\vec{C}\) in the first equation

We already have \(\vec{C} = \vec{A} + \vec{B}\) from the first equation. Therefore, substituting this into the rearranged second equation gives:

\[ \vec{A} + \vec{B} = -(\vec{A} + \vec{B}) \]

### Step 3: Analyze the equation

This implies:

\[ \vec{A} + \vec{B} + \vec{A} + \vec{B} = 0 \implies 2(\vec{A} + \vec{B}) = 0 \]

Thus, we can conclude:

\[ \vec{A} + \vec{B} = 0 \implies \vec{B} = -\vec{A} \]

### Step 4: Find the angle between \(\vec{A}\) and \(\vec{B}\)

Since \(\vec{B} = -\vec{A}\), the angle between \(\vec{A}\) and \(\vec{B}\) is \(180^\circ\) or \(\pi\) radians.

### Conclusion

The angle between vectors \(\vec{A}\) and \(\vec{B}\) is:

\[ \theta = \pi \text{ radians} \]