Reduce the equation of line `x-y+2z=5a d n3x+y+z=6` in symmetrical form. Or Find the line of intersection of planes `x-y+2z=5a n d3x+y+z=6.`

Explanation

To find the line of intersection of the planes given by the equations \(x - y + 2z = 5\) and \(3x + y + z = 6\), we will follow these steps:

### Step 1: Identify the Direction Ratios
The line of intersection of two planes can be represented by a direction vector that is perpendicular to the normals of both planes. The normal vector of the first plane \(x - y + 2z = 5\) is \(\vec{n_1} = (1, -1, 2)\) and the normal vector of the second plane \(3x + y + z = 6\) is \(\vec{n_2} = (3, 1, 1)\).

To find the direction ratios of the line of intersection, we can take the cross product of these two normal vectors:

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