(Solved): Homework IV: Problem 3 (20 points) The distance \( d \) of a point \( P \) to the line through poin ...

Homework IV: Problem 3 (20 points) The distance \( d \) of a point \( P \) to the line through points \( A \) and \( B \) is the length of the component of \( \overrightarrow{A P} \) that is orthogonal to \( \overrightarrow{A B} \), as indicated in the diagram. So the distance from \( P=(5,-4,1) \) to the line through the points \( A=(-1,-2,2) \) and \( B=(0,-5,0) \) is