What is the angle between `vec(a)` and `vec(b)` :
(i) Magnitude of `vec(a)` and `vec(b)` are `3` and `4` respectively.
(ii) Area of triangle made by `vec(a)` and `vec(b)` is 10.

Options

A. Question can be solved by information I only.
B. Question can be solved by information II only
C. Question can be solved by information I and II in combined form only.
D. Question can not be solved by both the informations only.

Answer

To find the angle between the vectors \(\vec{a}\) and \(\vec{b}\), we can use the information provided about their magnitudes and the area of the triangle formed by them.

### Step-by-Step Solution:

1. **Identify the given values:**
- Magnitude of \(\vec{a}\) = 3
- Magnitude of \(\vec{b}\) = 4
- Area of triangle formed by \(\vec{a}\) and \(\vec{b}\) = 10

2. **Use the formula for the area of a triangle formed by two vectors:**
The area \(A\) of the triangle formed by two vectors \(\vec{a}\) and \(\vec{b}\) can be expressed as:
\[ A = \frac{1}{2} |\vec{a} \times \vec{b}| \]
where \(|\vec{a} \times \vec{b}|\) is the magnitude of the cross product of the vectors.

3. **Relate the area to the sine of the angle:**
The magnitude of the cross product can also be expressed in terms of the angle \(\theta\) between the vectors:
\[ |\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin \theta \]
Substituting this into the area formula gives:
\[ A = \frac{1}{2} |\vec{a}| |\vec{b}| \sin \theta \]

4. **Substitute the known values into the area formula:**
\[ 10 = \frac{1}{2} \times 3 \times 4 \times \sin \theta \]
Simplifying this gives:
\[ 10 = 6 \sin \theta \]

5. **Solve for \(\sin \theta\):**
\[ \sin \theta = \frac{10}{6} = \frac{5}{3} \]
However, since the sine function cannot exceed 1, this indicates that the given area cannot be achieved with the given magnitudes of the vectors. Therefore, the information provided is insufficient to determine the angle.

6. **Conclusion:**
Since the sine of the angle exceeds 1, it implies that the area of the triangle cannot be formed with the given magnitudes of the vectors. Thus, we conclude that the problem cannot be solved with the given information.

### Final Answer:
The angle between \(\vec{a}\) and \(\vec{b}\) cannot be determined with the given information.