If ` vec a=5 hat i- hat j-3 hat k` , `vec b= hat i+3 hat j-5 hat k` then show that the vectors ` vec a+ vec b` , `vec a- vec b` are perpendicular.

Explanation

To show that the vectors \( \vec{a} + \vec{b} \) and \( \vec{a} - \vec{b} \) are perpendicular, we need to demonstrate that their dot product is zero.

### Step-by-Step Solution:

1. **Define the Vectors:**
Given:
\[
\vec{a} = 5 \hat{i} - \hat{j} - 3 \hat{k}
...