Find the direction ratios of this plane `2x-3y+4z+2=0`

Answer

To find the direction ratios of the plane given by the equation \(2x - 3y + 4z + 2 = 0\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the equation of the plane**: The given equation is \(2x - 3y + 4z + 2 = 0\).

2. **Rewrite the equation in standard form**: The standard form of a plane is given by \(Ax + By + Cz + D = 0\), where \(A\), \(B\), and \(C\) are the coefficients of \(x\), \(y\), and \(z\) respectively. In our case, we can identify:
- \(A = 2\)
- \(B = -3\)
- \(C = 4\)
- \(D = 2\) (though \(D\) is not needed for finding direction ratios).

3. **Determine the direction ratios**: The direction ratios of the plane are the coefficients of \(x\), \(y\), and \(z\) from the equation of the plane. Therefore, the direction ratios are:
- Direction ratios \(= (A, B, C) = (2, -3, 4)\).

4. **Conclusion**: Thus, the direction ratios of the plane \(2x - 3y + 4z + 2 = 0\) are \(2\), \(-3\), and \(4\).

### Final Answer:
The direction ratios of the plane are \(2, -3, 4\).

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