If `veca` and `vecb` are two unit vectors such that `veca+2vecb` and `5veca-4vecb` are perpendicular to each other, then the angle between `veca` and `vecb` is

Explanation

To solve the problem, we need to find the angle between two unit vectors \(\vec{a}\) and \(\vec{b}\) given that the vectors \(\vec{a} + 2\vec{b}\) and \(5\vec{a} - 4\vec{b}\) are perpendicular to each other.

### Step-by-Step Solution:

1. **Understanding the Condition of Perpendicularity**:
Two vectors are perpendicular if their dot product is zero. Therefore, we can write:
\[
(\vec{a} + 2\vec{b}) \cdot (5\vec{a} - 4\vec{b}) = 0
...