If vectors `vec(a) = 3 hat(i) + hat(j) - 2 hat(k)` and `vec(b) = hat(i) + lambda(j) - 3 hat (k)` are perpendicular to each other , find the value of `lambda`.

Explanation

To find the value of \( \lambda \) such that the vectors \( \vec{a} \) and \( \vec{b} \) are perpendicular, we can use the property that two vectors are perpendicular if their dot product is zero.

### Step 1: Write down the vectors
Given:
\[ \vec{a} = 3\hat{i} + \hat{j} - 2\hat{k} \]
\[
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