If ` veca + vecb = vecc and a^(2) + b^(2) =c^(2)` , then prove that ` veca and vecb` are prependicular to each other .

Explanation

To prove that vectors \(\vec{a}\) and \(\vec{b}\) are perpendicular given that \(\vec{a} + \vec{b} = \vec{c}\) and \(a^2 + b^2 = c^2\), we can follow these steps:

### Step 1: Understand the relationship between vectors
We know that if \(\vec{a} + \vec{b} = \vec{c}\), then the magnitude of vector \(\vec{c}\) can be expressed in terms of vectors \(\vec{a}\) and \(\vec{b}\).

### Step 2: Write the expression for the magnitude of \(\vec{c}\)
The magnitude of the resultant vector \(\vec{c}\) can be expressed using the formula:
\[
...