Find Cartesian and vector equation of the line which passes through the point `(-2,4,-5)` and parallel to the line given by `(x+3)/3=(y-4)/5=(z+8)/6` .

Explanation

To find the Cartesian and vector equations of the line that passes through the point \((-2, 4, -5)\) and is parallel to the line given by \(\frac{x+3}{3} = \frac{y-4}{5} = \frac{z+8}{6}\), we can follow these steps:

### Step 1: Identify the Direction Ratios
The given line's equation can be rewritten in the standard form to identify the direction ratios. From the equation \(\frac{x+3}{3} = \frac{y-4}{5} = \frac{z+8}{6}\), we can see that the direction ratios (or direction numbers) are \(3, 5, 6\).

### Step 2: Write the Cartesian Equation
The Cartesian equation of a line can be expressed as:
\[
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