(Solved): Consider the planes \( 1 x+2 y+5 z=1 \) and \( 1 x+5 z=0 \). (A) Find the unique point \( P \) on ...

Consider the planes \( 1 x+2 y+5 z=1 \) and \( 1 x+5 z=0 \). (A) Find the unique point \( P \) on the \( y \)-axis which is on both planes. (B) Find a unit vector \( \mathbf{u} \) with positive first coordinate that is parallel to both planes. \[ \mathbf{u}=\mathbf{i}+\mathbf{j}+\mathbf{k} \] (C) Use parts (A) and (B) to find a vector equation for the line of intersection of the two planes. \[ \mathbf{r}(t)=\mathbf{i}+\mathbf{j}+\mathbf{k} \]