If `|veca - vecb|=|veca| =|vecb|=1 ` , then the angle between ` veca and vecb` , is

Options

A. `pi/3`
B. ` ( 3pi)/4`
C. ` pi/2`
D. 0

Explanation

To solve the problem, we need to find the angle between the vectors \(\vec{a}\) and \(\vec{b}\) given the conditions \( |\vec{a} - \vec{b}| = |\vec{a}| = |\vec{b}| = 1 \).

### Step-by-Step Solution:

1. **Understand the Given Information:**
We know that:
\[ |\vec{a}| = 1, \quad |\vec{b}| = 1, \quad |\vec{a} - \vec{b}| = 1 \]

2. **Use the Magnitude Formula:**
We can express the magnitude of the difference of two vectors:
\[ |\vec{a} - \vec{b}|^2 = |\vec{a}|^2 + |\vec{b}|^2 - 2 \vec{a} \cdot \vec{b} \]

3. **Substitute the Known Values:**
Since \( |\vec{a}| = 1 \) and \( |\vec{b}| = 1 \), we have:
\[ |\vec{a} - \vec{b}|^2 = 1^2 + 1^2 - 2 \vec{a} \cdot \vec{b} \]
This simplifies to:
\[ |\vec{a} - \vec{b}|^2 = 1 + 1 - 2 \vec{a} \cdot \vec{b} \]
Therefore:
\[ |\vec{a} - \vec{b}|^2 = 2 - 2 \vec{a} \cdot \vec{b} \]

4. **Set the Equation:**
Since \( |\vec{a} - \vec{b}| = 1 \), we square both sides:
\[ 1^2 = 2 - 2 \vec{a} \cdot \vec{b} \]
This gives us:
\[ 1 = 2 - 2 \vec{a} \cdot \vec{b} \]

5. **Rearrange the Equation:**
Rearranging the equation leads to:
\[ 2 \vec{a} \cdot \vec{b} = 2 - 1 \]
Thus:
\[ 2 \vec{a} \cdot \vec{b} = 1 \]
Therefore:
\[ \vec{a} \cdot \vec{b} = \frac{1}{2} \]

6. **Relate the Dot Product to the Angle:**
The dot product can also be expressed in terms of the angle \(\theta\) between the vectors:
\[ \vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \theta \]
Substituting the magnitudes:
\[ \vec{a} \cdot \vec{b} = 1 \cdot 1 \cdot \cos \theta = \cos \theta \]
Therefore, we have:
\[ \cos \theta = \frac{1}{2} \]

7. **Find the Angle:**
The angle \(\theta\) that satisfies \(\cos \theta = \frac{1}{2}\) is:
\[ \theta = \frac{\pi}{3} \text{ radians} \quad \text{(or } 60^\circ\text{)} \]

### Final Answer:
The angle between \(\vec{a}\) and \(\vec{b}\) is \(\frac{\pi}{3}\) radians.

---