For the resultant of two vectors to be maximum , what must be the angle between them ?

Options

A. `0^(@)`
B. `60^(@)`
C. `90^(@)`
D. `180^(@)`

Explanation

To determine the angle between two vectors for their resultant to be maximum, we can follow these steps:

### Step 1: Understand the Resultant of Two Vectors
When two vectors, say **A** and **B**, are combined, the resultant vector **R** can be calculated using the formula:
\[ R = \sqrt{A^2 + B^2 + 2AB \cos \theta} \]
where \( \theta \) is the angle between the two vectors.

### Step 2: Analyze the Cosine Function
The term \( \cos \theta \) plays a crucial role in determining the magnitude of the resultant vector. The value of \( \cos \theta \) ranges from -1 to +1. To maximize the resultant vector \( R \), we need to maximize the value of \( \cos \theta \).

### Step 3: Find the Maximum Value of Cosine
The maximum value of \( \cos \theta \) is 1, which occurs when:
\[ \theta = 0^\circ \]

### Step 4: Substitute Back to the Resultant Formula
When \( \theta = 0^\circ \), the formula for the resultant becomes:
\[ R = \sqrt{A^2 + B^2 + 2AB \cdot 1} = \sqrt{A^2 + B^2 + 2AB} \]
This shows that the magnitude of the resultant vector is maximized when the two vectors are aligned in the same direction.

### Conclusion
Thus, for the resultant of two vectors to be maximum, the angle between them must be:
\[ \theta = 0^\circ \]

### Final Answer
The angle between the two vectors for maximum resultant is **0 degrees**.

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