Find the value of `m` for which thestraight line `3x-2y+z+3=0=4x=3y+4z+1` is parallel to the plane `2x-y+m z-2=0.`

Explanation

To find the value of \( m \) for which the straight line defined by the equations \( 3x - 2y + z + 3 = 0 \) and \( 4x - 3y + 4z + 1 = 0 \) is parallel to the plane defined by the equation \( 2x - y + mz - 2 = 0 \), we will follow these steps:

### Step 1: Identify the normal vectors of the planes
The equations of the two planes are:
- Plane 1: \( 3x - 2y + z + 3 = 0 \)
- Plane 2: \( 4x - 3y + 4z + 1 = 0 \)

The normal vector \( \mathbf{n_1} \) for Plane 1 is \( (3, -2, 1) \) and for Plane 2 is \( (4, -3, 4) \).
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