Find the vector of a line passing through `(2,-1,1)` and parallel to the line whose equations are `(x-3)/2=(y+1)/7=(z-2)/(-3)dot`

Explanation

To find the vector equation of a line passing through the point \( (2, -1, 1) \) and parallel to the line given by the equations \( \frac{x-3}{2} = \frac{y+1}{7} = \frac{z-2}{-3} \), we can follow these steps:

### Step 1: Identify the Direction Ratios
The direction ratios of the given line can be extracted from the equation. The equation \( \frac{x-3}{2} = \frac{y+1}{7} = \frac{z-2}{-3} \) indicates that the direction ratios are \( 2, 7, -3 \).

**Hint:** Look for the coefficients in the parametric form of the line equation to identify the direction ratios.

### Step 2: Write the Point and Direction Ratios
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