The Cartesian equation of a line is `(x-3)/2=(y+1)/(-2)=(z-3)/5` . Find the vector equation of the line.

Explanation

To find the vector equation of the line given in Cartesian form, we can follow these steps:

### Step 1: Identify the point on the line
From the given Cartesian equation of the line:
\[ \frac{x-3}{2} = \frac{y+1}{-2} = \frac{z-3}{5} \]
we can see that the line passes through the point where \(x = 3\), \(y = -1\), and \(z = 3\). Thus, the point on the line is:
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