diff --git a/Chapters/chapter2.tex b/Chapters/chapter2.tex
index 33ba6e4..ca344d4 100644
--- a/Chapters/chapter2.tex
+++ b/Chapters/chapter2.tex
@@ -583,7 +583,8 @@ \subsection{Projections and Unit Vectors}
 compute $s$, we use the fact that the vector ${\rm proj}_\bb\aa - \aa$
 (along the dotted line in the diagram) is orthogonal to $\bb$. Thus
 $({\rm proj}_\bb\aa - \aa)\cdot\bb = 0$, or $(s\bb-\aa)\cdot\bb=0$, or
-$s = \aa\cdot\bb / \bb\cdot\bb = \aa\cdot\bb / \|\bb\|^2$. Thus
+$(s\bb)\cdot\bb-\aa\cdot\bb=0$, or $s(\bb\cdot\bb)=\aa\cdot\bb=$, or
+$s = (\aa\cdot\bb) / (\bb\cdot\bb) = (\aa\cdot\bb) / \|\bb\|^2$. Thus
 \begin{equation}
 \label{eq:projection}
 {\rm proj}_\bb\aa = {{\aa\cdot\bb}\over{\|\bb\|^2}}\bb.
diff --git a/notes.tex b/notes.tex
index 26956b0..e191657 100644
--- a/notes.tex
+++ b/notes.tex
@@ -1,6 +1,6 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %                                                                 %
-%                            ROOT FILE        5                    %
+%                            ROOT FILE        5                   %
 %                                                                 %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%