Show that `|veca|vecb+|vecb|veca` is perpendicular to `|veca|vecb-|vecb|veca` for any two non zero vectors `veca and vecb.

Explanation

To show that \(|\vec{a}|\vec{b} + |\vec{b}|\vec{a}\) is perpendicular to \(|\vec{a}|\vec{b} - |\vec{b}|\vec{a}\) for any two non-zero vectors \(\vec{a}\) and \(\vec{b}\), we can use the property that two vectors are perpendicular if their dot product is zero.

### Step-by-step Solution:

1. **Define the Vectors**:
Let \(\vec{u} = |\vec{a}|\vec{b} + |\vec{b}|\vec{a}\) and \(\vec{v} = |\vec{a}|\vec{b} - |\vec{b}|\vec{a}\).

2. **Calculate the Dot Product**:
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