Find the equation of the plane through the intersection of the planes `3x-4y+5z=10a n d2x+2y-3z=4` and parallel to the line `x=2y=3zdot`

Explanation

To find the equation of the plane that passes through the intersection of the planes \(3x - 4y + 5z = 10\) and \(2x + 2y - 3z = 4\) and is parallel to the line given by \(x = 2y = 3z\), we can follow these steps:

### Step 1: Find the direction ratios of the line
The line given by \(x = 2y = 3z\) can be expressed in parametric form. Let \(t\) be the parameter:
- \(x = t\)
- \(y = \frac{t}{2}\)
- \(z = \frac{t}{3}\)

...