Find the value of m so that the vector `3hat(i)-2hat(j)+hat(k)` may be perpendicular to the vector `2hat(i)+6hat(j)+mhat(k)`.

Explanation

To find the value of \( m \) such that the vector \( \mathbf{A} = 3\hat{i} - 2\hat{j} + \hat{k} \) is perpendicular to the vector \( \mathbf{B} = 2\hat{i} + 6\hat{j} + m\hat{k} \), we can follow these steps:

### Step 1: Understand the condition for perpendicular vectors
Two vectors are perpendicular if their dot product is zero. Therefore, we need to set up the equation based on the dot product of the two vectors.

### Step 2: Write the dot product
The dot product \( \mathbf{A} \cdot \mathbf{B} \) is given by:
\[
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