Two unequal vectors are inclined at an angle `30^(@)`. When they are added, the resultant can be :

Options

A. zero
B. directed along either
C. directed opposite to either
D. represented by none of these

Answer

To solve the problem of adding two unequal vectors that are inclined at an angle of \(30^\circ\), we can follow these steps:

### Step 1: Understand the Problem
We have two unequal vectors, which we can denote as \(\vec{A}\) and \(\vec{B}\). The angle between them is given as \(30^\circ\).

### Step 2: Use the Parallelogram Law
According to the parallelogram law of vector addition, the resultant vector \(\vec{R}\) can be represented as the diagonal of a parallelogram formed by the two vectors \(\vec{A}\) and \(\vec{B}\).

### Step 3: Calculate the Magnitude of the Resultant
The magnitude of the resultant vector \(\vec{R}\) can be calculated using the formula:
\[ R = \sqrt{A^2 + B^2 + 2AB \cos(\theta)} \]
where \(A\) and \(B\) are the magnitudes of the vectors \(\vec{A}\) and \(\vec{B}\), and \(\theta\) is the angle between them, which is \(30^\circ\).

### Step 4: Analyze the Options
1. **Zero**: The resultant cannot be zero because the vectors are unequal and inclined at an angle.
2. **Directed along either**: The resultant cannot be directed along either vector since it is the diagonal of the parallelogram formed by the two vectors.
3. **Directed opposite to either**: The resultant cannot be directed opposite to either vector for the same reason as above.
4. **None of these**: This option is likely correct because the resultant does not fit any of the previous descriptions.

### Step 5: Conclusion
Since the resultant vector cannot be zero, directed along either vector, or directed opposite to either vector, the correct answer is that the resultant is represented by "none of these".

### Final Answer
The resultant can be represented by none of these options.

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