What should be the the angle ` theta` between two vectors `vec A and vec B` for their resultant ` vec R` to be (i) maximum (ii) minimum ? Give their resultant value.

Explanation

To find the angle \( \theta \) between two vectors \( \vec{A} \) and \( \vec{B} \) for their resultant \( \vec{R} \) to be maximum and minimum, we can use the formula for the magnitude of the resultant of two vectors:

\[ R = \sqrt{A^2 + B^2 + 2AB \cos \theta} \]

### Step 1: Maximum Resultant
To find the angle for the maximum resultant, we need to maximize the term \( \cos \theta \).
...