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(Solved):   Can someone solve this Linear Algebra question with as much explanation for the steps as po ...



9. (9 points) Consider the line \( L_{1}:\left\{\begin{array}{l}x=1+t \\ y=2+t \\ z=1-t\end{array}\right. \), and the point \

 

Can someone solve this Linear Algebra question with as much explanation for the steps as possible please.

9. (9 points) Consider the line \( L_{1}:\left\{\begin{array}{l}x=1+t \\ y=2+t \\ z=1-t\end{array}\right. \), and the point \( A(2,3,-6) \) (a) Find the point on \( L_{1} \), which is closest to the point \( A \). (b) Find the distance between the line \( L_{1} \), and the point \( A \). (c) Find the equation of the plane that contains the line \( L_{1} \), and the point \( B(1,2,2) \).


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(a) Here, The distance between any point on the line and point (2,3,?6) is
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