The Cartesian equation of a line is `(x+3)/2=(y-5)/4=(z+6)/2`. Find the vector equation for the line.

Explanation

To find the vector equation of the line given in Cartesian form as \((x+3)/2 = (y-5)/4 = (z+6)/2\), we can follow these steps:

### Step 1: Identify the Direction Ratios
From the given equation, we can identify the direction ratios of the line. The equation can be rewritten as:
\[ \frac{x + 3}{2} = \frac{y - 5}{4} = \frac{z + 6}{2} \]
From this, we can see that the direction ratios \(a\), \(b\), and \(c\) are:
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