From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 12 Feb 2019 05:31:00 +0000 (+1100)
Subject: perpendicular vector resolute
X-Git-Tag: yr12~255
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/1e6715bc8802242dce8fbb21c4e94ff318c2f344?hp=--cc

perpendicular vector resolute
---

1e6715bc8802242dce8fbb21c4e94ff318c2f344
diff --git a/spec/vectors.md b/spec/vectors.md
index db65983..ccdec2f 100644
--- a/spec/vectors.md
+++ b/spec/vectors.md
@@ -139,7 +139,8 @@ Vector resolute of $\boldsymbol{a}$ in direction of $\boldsymbol{b}$ is magnitud
 
 $$\boldsymbol{u}={{\boldsymbol{a}\cdot\boldsymbol{b}}\over |\boldsymbol{b}|^2}\boldsymbol{b}=\left({\boldsymbol{a}\cdot{\boldsymbol{b} \over |\boldsymbol{b}|}}\right)\left({\boldsymbol{b} \over |\boldsymbol{b}|}\right)=(\boldsymbol{a} \cdot \hat{\boldsymbol{b}})\hat{\boldsymbol{b}}$$
 
-Scalar resolute of $\vec{a}$ on $\vec{b} = |\vec{u}| = \vec{a} \cdot \hat{\vec{b}}$
+Scalar resolute of $\vec{a}$ on $\vec{b} = |\vec{u}| = \vec{a} \cdot \hat{\vec{b}}$ (results in a scalar)  
+Vector resolute of $\vec{a}$ perpendicular to $b$ is equal to $\vec{a} - \vec{u}$ where $\vec{u}$ is vector projection of $\vec{a}$ on $\vec{b}$
 
 ## Vector proofs