If ` veca=5 hat i- hat j-3 hat k`and ` vecb= hat i+3 hat j-5 hat k`then show that the vectors ` veca+ vecb`and ` veca- vecb`are perpendicular.

Explanation

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

### Step 1: Define the vectors
Given:
\[ \vec{a} = 5\hat{i} - \hat{j} - 3\hat{k} \]
\[
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