Find the vector equation of the line passing through the point `(2,-1,-1)` which is parallel to the line `6x-2=3y+1=2z-2.`

Explanation

To find the vector equation of the line that passes through the point \( (2, -1, -1) \) and is parallel to the line given by the equation \( 6x - 2 = 3y + 1 = 2z - 2 \), we can follow these steps:

### Step 1: Rewrite the given line in parametric form
The equation \( 6x - 2 = 3y + 1 = 2z - 2 \) can be rewritten in parametric form. We can set:
\[ 6x - 2 = t \quad \Rightarrow \quad x = \frac{t + 2}{6} \]
\[
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