Find the value of `lambda`. If the points `A(-1,3,2), B(-4,2,-2)` and `C(5,lambda,10)` are collinear.

Explanation

To find the value of \( \lambda \) such that the points \( A(-1, 3, 2) \), \( B(-4, 2, -2) \), and \( C(5, \lambda, 10) \) are collinear, we can follow these steps:

### Step 1: Understand the condition for collinearity
Three points \( A \), \( B \), and \( C \) are collinear if the vectors \( \overrightarrow{AB} \) and \( \overrightarrow{AC} \) are parallel. This can be expressed mathematically as:
\[ \overrightarrow{AB} = B - A = (-4 + 1, 2 - 3, -2 - 2) = (-3, -1, -4) \]
\[
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