collinearity

diff --git a/spec/vectors.md b/spec/vectors.md
index 0b6ea2a591579df2297f0fbb2caefea27642e9e6..db6598373fc53fe2f011284825156c99d00539e8 100644 (file)
--- a/spec/vectors.md
+++ b/spec/vectors.md
@@ -139,6 +139,8 @@ Vector resolute of $\boldsymbol{a}$ in direction of $\boldsymbol{b}$ is magnitud
 
 $$\boldsymbol{u}={{\boldsymbol{a}\cdot\boldsymbol{b}}\over |\boldsymbol{b}|^2}\boldsymbol{b}=\left({\boldsymbol{a}\cdot{\boldsymbol{b} \over |\boldsymbol{b}|}}\right)\left({\boldsymbol{b} \over |\boldsymbol{b}|}\right)=(\boldsymbol{a} \cdot \hat{\boldsymbol{b}})\hat{\boldsymbol{b}}$$
 
 
 $$\boldsymbol{u}={{\boldsymbol{a}\cdot\boldsymbol{b}}\over |\boldsymbol{b}|^2}\boldsymbol{b}=\left({\boldsymbol{a}\cdot{\boldsymbol{b} \over |\boldsymbol{b}|}}\right)\left({\boldsymbol{b} \over |\boldsymbol{b}|}\right)=(\boldsymbol{a} \cdot \hat{\boldsymbol{b}})\hat{\boldsymbol{b}}$$
 

+Scalar resolute of $\vec{a}$ on $\vec{b} = |\vec{u}| = \vec{a} \cdot \hat{\vec{b}}$
+

 ## Vector proofs
 
 **Concurrent lines -** $\ge$ 3 lines intersect at a single point  
 ## Vector proofs
 
 **Concurrent lines -** $\ge$ 3 lines intersect at a single point  


@@ -175,3 +177,6 @@ $$\cos \alpha = {a_1 \over |\vec{a}|}, \quad \cos \beta = {a_2 \over |\vec{a}|},
 
 **on CAS:** `angle([a b c], [1 0 0])` for angle between $a\vec{i} + b\vec{j} + c\vec{k}$ and $x$-axis
 
 
 **on CAS:** `angle([a b c], [1 0 0])` for angle between $a\vec{i} + b\vec{j} + c\vec{k}$ and $x$-axis
 

+## Collinearity
+
+Points $A, B, C$ are collinear iff $\vec{AC}=m\vec{AB} \text{ where } m \ne 0$