Two equal vector have a resultant equal to either of them, then the angle between them will be:

Options

A. `60^(@)`
B. `120^(@)`0
C. `90^(@)`
D. `0^(@)`

Explanation

To solve the problem of finding the angle between two equal vectors whose resultant is equal to either of them, we can follow these steps:

### Step 1: Define the vectors
Let the two equal vectors be represented as **A** and **B**. Since they are equal, we can say:
- |A| = |B| = x (where x is the magnitude of the vectors).

### Step 2: Write the formula for the resultant of two vectors
The resultant **R** of two vectors **A** and **B** can be calculated using the formula:
\[ R = \sqrt{A^2 + B^2 + 2AB \cos(\theta)} \]
Where:
- A = |A| = x
- B = |B| = x
- θ = angle between A and B

### Step 3: Substitute the values
Substituting the magnitudes of the vectors into the resultant formula gives:
\[ R = \sqrt{x^2 + x^2 + 2x^2 \cos(\theta)} \]
This simplifies to:
\[ R = \sqrt{2x^2 + 2x^2 \cos(\theta)} \]

### Step 4: Simplify the expression
Factoring out the common terms:
\[ R = \sqrt{2x^2(1 + \cos(\theta))} \]
This can be further simplified to:
\[ R = x \sqrt{2(1 + \cos(\theta))} \]

### Step 5: Set the resultant equal to the magnitude of the vectors
According to the problem, the resultant is equal to the magnitude of either vector:
\[ R = x \]
Thus, we have:
\[ x = x \sqrt{2(1 + \cos(\theta))} \]

### Step 6: Divide both sides by x (assuming x ≠ 0)
Dividing both sides by x gives:
\[ 1 = \sqrt{2(1 + \cos(\theta))} \]

### Step 7: Square both sides
Squaring both sides results in:
\[ 1 = 2(1 + \cos(\theta)) \]

### Step 8: Solve for cos(θ)
Rearranging the equation gives:
\[ 1 = 2 + 2\cos(\theta) \]
\[ 2\cos(\theta) = 1 - 2 \]
\[ 2\cos(\theta) = -1 \]
\[ \cos(\theta) = -\frac{1}{2} \]

### Step 9: Find the angle θ
The angle θ for which cos(θ) = -1/2 is:
\[ \theta = 120^\circ \]

### Conclusion
Thus, the angle between the two equal vectors is **120 degrees**.

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