The equation of line is ` 2x - 2 = 3y + 1 = 6z - 2 `
find its direction ratios and also find the vector
equation of the line .

Explanation

To solve the problem step by step, we will first extract the direction ratios from the given equation of the line and then find the vector equation of the line.

### Step 1: Understand the given equation
The equation of the line is given as:
\[ 2x - 2 = 3y + 1 = 6z - 2 \]

### Step 2: Rewrite the equation
We can rewrite the equation in a more manageable form by setting it equal to a parameter \( t \):
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