Show that each of the given three vectors is a unit vector: `1/7(2 hat i+3 hat j+6 hat k),1/7(3 hat i-6 hat j+2 hat k),1/7(6 hat i+2 hat j-3 hat k)`Also, show that they are mutually perpendicular to each other.

Explanation

To show that each of the given three vectors is a unit vector and that they are mutually perpendicular to each other, we will follow these steps:

### Step 1: Verify if the vectors are unit vectors

The vectors given are:
1. \( \mathbf{A} = \frac{1}{7}(2 \hat{i} + 3 \hat{j} + 6 \hat{k}) \)
2. \( \mathbf{B} = \frac{1}{7}(3 \hat{i} - 6 \hat{j} + 2 \hat{k}) \)
3. \( \mathbf{C} = \frac{1}{7}(6 \hat{i} + 2 \hat{j} - 3 \hat{k}) \)
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