If the point A ( `lamda` , 5 , -2) lies on the line ` (x + 1)/(7) = ( y + 1)/(- 6) = ( z + 1)/(1)`, then the value of `lamda` is

Answer

To find the value of \( \lambda \) for the point \( A(\lambda, 5, -2) \) lying on the line given by the equation

\[ \frac{x + 1}{7} = \frac{y + 1}{-6} = \frac{z + 1}{1}, \]

we will substitute the coordinates of point \( A \) into the equation of the line.

### Step 1: Substitute the coordinates into the line equation

We know that the point \( A \) has coordinates \( (\lambda, 5, -2) \). We can substitute these values into the line equation:

\[ \frac{\lambda + 1}{7} = \frac{5 + 1}{-6} = \frac{-2 + 1}{1}. \]

### Step 2: Simplify the right-hand side

Now, let's simplify the right-hand side:

1. Calculate \( \frac{5 + 1}{-6} \):
\[ \frac{6}{-6} = -1. \]

2. Calculate \( \frac{-2 + 1}{1} \):
\[ \frac{-1}{1} = -1. \]

So, we have:

\[ \frac{\lambda + 1}{7} = -1. \]

### Step 3: Solve for \( \lambda \)

Now we can solve for \( \lambda \):

1. Multiply both sides by 7 to eliminate the fraction:
\[ \lambda + 1 = -7. \]

2. Subtract 1 from both sides:
\[ \lambda = -7 - 1 = -8. \]

### Conclusion

The value of \( \lambda \) is

\[ \lambda = -8. \]

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