If \(P(x,y,z)\) is the intersection of the lines
\[
\vec r=(2\hat i-2\hat j+3\hat k)+t(\hat i-3\hat j+\hat k)
\]
and
\[
\vec r=(2\hat j-\hat k)+s(\hat i-\hat j+3\hat k),
\]
then \(x+y+z=\)
Show Hint
To find the intersection of two vector equations of lines, equate the corresponding coordinates and solve the resulting system of equations for the parameters.