if vectors `3 hat i -`2 `hat j +`m `hat k and - 2 hat i+ hat j+ `4 hat k are perpendicular to each other , find the value of m

Explanation

To solve the problem, we need to find the value of \( m \) such that the vectors \( \vec{A} = 3\hat{i} - 2\hat{j} + m\hat{k} \) and \( \vec{B} = -2\hat{i} + \hat{j} + 4\hat{k} \) are perpendicular to each other. Two vectors are perpendicular if their dot product is zero.

### Step-by-Step Solution:

1. **Write down the vectors:**
\[ \vec{A} = 3\hat{i} - 2\hat{j} + m\hat{k} \]
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