Find the equation of a plane containing the line of intersection of the planes `x+y+z-6=0a n d2x+3y+4z+5=0` passing through `(1,1,1)` .

Options

A. `20x+23y+26z-69=0`
B. `20x+26y+23z-69=0`
C. `x+y+z-3=0`
D. `2x+3y+4z-9=0`

Explanation

To find the equation of a plane containing the line of intersection of the planes \(x + y + z - 6 = 0\) and \(2x + 3y + 4z + 5 = 0\) and passing through the point \((1, 1, 1)\), we can follow these steps:

### Step 1: Write the general equation of the plane
The equation of a plane that contains the line of intersection of two planes can be expressed as a linear combination of their equations. Thus, we can write the equation of the desired plane as:
\[ x + y + z - 6 + \lambda(2x + 3y + 4z + 5) = 0 \]
where \(\lambda\) is a parameter.
...