The value of `lamda` for which the lines `(x-1)/1=(y-2)/(lamda)=(z+1)/(-1)` and `(x+1)/(-lamda)=(y+1)/2=(z-2)/1` are perpendicular to each other is

Options

A. 0
B. 1
C. -1
D. none of these

Explanation

To find the value of \( \lambda \) for which the given lines are perpendicular, we can follow these steps:

### Step 1: Identify the direction ratios of the lines
The given lines are represented in symmetric form. We can extract the direction ratios from these equations.

For the first line:
\[ \frac{x-1}{1} = \frac{y-2}{\lambda} = \frac{z+1}{-1} \]
The direction ratios (denoted as \( V_1 \)) are:
\[ 1, \lambda, -1 \]

For the second line:
\[ \frac{x+1}{-\lambda} = \frac{y+1}{2} = \frac{z-2}{1} \]
The direction ratios (denoted as \( V_2 \)) are:
\[ -\lambda, 2, 1 \]

### Step 2: Use the condition for perpendicularity
Two lines are perpendicular if the dot product of their direction ratios is zero. Therefore, we need to calculate the dot product \( V_1 \cdot V_2 \):
\[ V_1 \cdot V_2 = (1)(-\lambda) + (\lambda)(2) + (-1)(1) \]
This simplifies to:
\[ -\lambda + 2\lambda - 1 = 0 \]

### Step 3: Solve the equation
Now, we simplify the equation:
\[ \lambda - 1 = 0 \]
Thus, we find:
\[ \lambda = 1 \]

### Conclusion
The value of \( \lambda \) for which the lines are perpendicular is:
\[ \lambda = 1 \]

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