If `veca . vecb` =ab then the angle between `veca` and `vecb` is

Options

A. `pi//2`
B. `pi`
C. zero
D. any angle between zero and `pi`

Answer

To solve the problem, we need to find the angle between two vectors \(\vec{a}\) and \(\vec{b}\) given that their dot product \(\vec{a} \cdot \vec{b} = ab\), where \(a\) and \(b\) are the magnitudes of the vectors \(\vec{a}\) and \(\vec{b}\).

### Step-by-step Solution:

1. **Understand the Dot Product Formula**:
The dot product of two vectors \(\vec{a}\) and \(\vec{b}\) is given by the formula:
\[ \vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \theta \]
where \(\theta\) is the angle between the two vectors.

2. **Set Up the Given Equation**:
According to the problem, we have:
\[ \vec{a} \cdot \vec{b} = ab \]
Here, \(a = |\vec{a}|\) and \(b = |\vec{b}|\).

3. **Substitute into the Dot Product Formula**:
From the dot product formula, we can substitute:
\[ |\vec{a}| |\vec{b}| \cos \theta = ab \]
Since \(a = |\vec{a}|\) and \(b = |\vec{b}|\), we can rewrite this as:
\[ ab \cos \theta = ab \]

4. **Simplify the Equation**:
We can divide both sides of the equation by \(ab\) (assuming \(a\) and \(b\) are not zero):
\[ \cos \theta = 1 \]

5. **Find the Angle \(\theta\)**:
The cosine of an angle is equal to 1 when the angle is:
\[ \theta = 0 \text{ radians} \quad (\text{or } 0^\circ) \]

### Conclusion:
The angle between the vectors \(\vec{a}\) and \(\vec{b}\) is \(0\) radians (or \(0^\circ\)), meaning the vectors are in the same direction.