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.`

Options

A. -2
B. 8
C. -18
D. 11

Explanation

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

### Step 1: Find the Direction Ratios of the Line
The direction ratios of the line can be derived from the normal vectors of the two planes given by the equations of the line.

1. The first plane \( 3x - 2y + z + 3 = 0 \) has a normal vector \( \mathbf{n_1} = (3, -2, 1) \).
2. The second plane \( 4x + 3y + 4z + 1 = 0 \) has a normal vector \( \mathbf{n_2} = (4, 3, 4) \).

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