To find the direction ratios of the line that is perpendicular to the lines with direction ratios (-1, 2, 2) and (0, 2, 1), we can follow these steps:
### Step 1: Define the Direction Ratios as Vectors
Let the direction ratios of the first line be represented as vector **b1**:
\[
\mathbf{b1} = (-1, 2, 2) = -1 \mathbf{i} + 2 \mathbf{j} + 2 \mathbf{k}
\]
Let the direction ratios of the second line be represented as vector **b2**:
\[
\mathbf{b2} = (0, 2, 1) = 0 \mathbf{i} + 2 \mathbf{j} + 1 \mathbf{k}
\]
### Step 2: Use the Cross Product to Find the Perpendicular Vector
To find a vector that is perpendicular to both **b1** and **b2**, we can take the cross product of these two vectors:
\[
\mathbf{b} = \mathbf{b1} \times \mathbf{b2}
\]
### Step 3: Set Up the Determinant for the Cross Product
The cross product can be calculated using the determinant of a matrix:
\[
\mathbf{b} = \begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
-1 & 2 & 2 \\
0 & 2 & 1
\end{vmatrix}
\]
### Step 4: Calculate the Determinant
Calculating the determinant, we have:
\[
\mathbf{b} = \mathbf{i} \begin{vmatrix} 2 & 2 \\ 2 & 1 \end{vmatrix} - \mathbf{j} \begin{vmatrix} -1 & 2 \\ 0 & 1 \end{vmatrix} + \mathbf{k} \begin{vmatrix} -1 & 2 \\ 0 & 2 \end{vmatrix}
\]
Calculating each of the 2x2 determinants:
1. For **i** component:
\[
\begin{vmatrix} 2 & 2 \\ 2 & 1 \end{vmatrix} = (2 \cdot 1) - (2 \cdot 2) = 2 - 4 = -2
\]
2. For **j** component:
\[
\begin{vmatrix} -1 & 2 \\ 0 & 1 \end{vmatrix} = (-1 \cdot 1) - (2 \cdot 0) = -1 - 0 = -1
\]
3. For **k** component:
\[
\begin{vmatrix} -1 & 2 \\ 0 & 2 \end{vmatrix} = (-1 \cdot 2) - (2 \cdot 0) = -2 - 0 = -2
\]
Putting it all together:
\[
\mathbf{b} = -2 \mathbf{i} - (-1) \mathbf{j} - 2 \mathbf{k} = -2 \mathbf{i} + 1 \mathbf{j} - 2 \mathbf{k}
\]
### Step 5: Write the Direction Ratios
Thus, the direction ratios of the line that is perpendicular to the given lines are:
\[
\mathbf{b} = (-2, 1, -2)
\]
### Final Answer
The direction ratios of the line which is perpendicular to the lines with direction ratios (-1, 2, 2) and (0, 2, 1) are:
\[
\boxed{(-2, 1, -2)}
\]
