Find the value of `lambda` so that the following lines are perpendicular to each other. `(x-5)/(5lambda+2)=(2-y)/5=(1-z)/(-1), x/1=(2y+1)/(4lambda)=(1-z)/(-3)`

Explanation

To find the value of \( \lambda \) such that the given lines are perpendicular to each other, we will follow these steps:

### Step 1: Write the equations of the lines in standard form
The equations of the lines are given as:
1. \( \frac{x-5}{5\lambda + 2} = \frac{2-y}{5} = \frac{1-z}{-1} \)
2. \( \frac{x}{1} = \frac{2y+1}{4\lambda} = \frac{1-z}{-3} \)

We can rewrite these equations in the parametric form.
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