Direction-ratios of normal to plane which is parallel to the plane 3x + y - z = 11 are ,

Options

A. `lt 3, 1, - 1 gt `
B. `lt 0 , 1, 1 gt`
C. `lt - 3, 1, -1, gt`
D. `lt 1 , 1, 0 gt`

Answer

To find the direction ratios of the normal to a plane that is parallel to the given plane \(3x + y - z = 11\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Normal Vector of the Given Plane:**
The equation of the plane is given in the form \(Ax + By + Cz = D\). For the plane \(3x + y - z = 11\), the coefficients \(A\), \(B\), and \(C\) represent the direction ratios of the normal to the plane. Thus, the normal vector is given by:
\[ \text{Normal Vector} = (A, B, C) = (3, 1, -1) \]

2. **Understand the Concept of Parallel Planes:**
Two planes are parallel if their normal vectors are the same or scalar multiples of each other. Therefore, any plane that is parallel to the given plane will have the same normal vector.

3. **Write the Direction Ratios of the Normal to the Parallel Plane:**
Since the direction ratios of the normal to the plane are the same for any plane parallel to it, the direction ratios for the normal to the parallel plane will also be:
\[ (3, 1, -1) \]

4. **Conclusion:**
Therefore, the direction ratios of the normal to the plane which is parallel to the plane \(3x + y - z = 11\) are:
\[ \boxed{(3, 1, -1)} \]