Find the vector equation of the line which is parallel to the vector `3hati-2hatj+6hatk` and which passes through the point `(1,-2,3)`.

Explanation

To find the vector equation of the line that is parallel to the vector \( \mathbf{b} = 3\hat{i} - 2\hat{j} + 6\hat{k} \) and passes through the point \( (1, -2, 3) \), we can follow these steps:

### Step 1: Identify the point and the direction vector
The point through which the line passes is given as \( (1, -2, 3) \). We can represent this point as a position vector:
\[ \mathbf{A} = 1\hat{i} - 2\hat{j} + 3\hat{k} \]
The direction vector of the line is given as:
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