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

Explanation

To solve the problem, we will break it down into steps to find the direction ratios and the vector equation of the line given by the Cartesian equations \(6x - 2 = 3y + 1 = 2z - 2\).

### Step 1: Rewrite the Cartesian equations
The given equations can be rewritten as:
\[ 6x - 2 = 3y + 1 = 2z - 2 \]
We can set each part equal to a parameter \(t\):
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