For what value of (m), the vector `vec A =2 hat I + 3 hat j -6 hat j` is perpendicular to ` vec B =3 hati-m hat j + 6 hat k?`

Explanation

To determine the value of \( m \) 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 equal to zero.

### Step-by-Step Solution:

1. **Identify the vectors:**
\[ \vec{A} = 2 \hat{i} + 3 \hat{j} - 6 \hat{k} \]
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