vector projections and axes

diff --git a/spec/vectors.md b/spec/vectors.md
index 6218b24ed369c915ef0a331990c177d91e295cc7..0a95e9eff152342b310bb2ed179f5cabfaf30907 100644 (file)
--- a/spec/vectors.md
+++ b/spec/vectors.md
@@ -152,3 +152,15 @@ $$\therefore \vec{c} = m\vec{a} + n\vec{b} \quad \text{(simultaneous)}$$
 $\vec{a}, \vec{b},$ and $\vec{c}$ are linearly independent if no vector in the set is expressible as a linear combination of other vectors in set, or if they are parallel.
 
 Vector $\vec{w}$ is a linear combination of vectors $\vec{v_1}, \vec{v_2}, \vec{v_3}$
 $\vec{a}, \vec{b},$ and $\vec{c}$ are linearly independent if no vector in the set is expressible as a linear combination of other vectors in set, or if they are parallel.
 
 Vector $\vec{w}$ is a linear combination of vectors $\vec{v_1}, \vec{v_2}, \vec{v_3}$

+
+## Three-dimensional vectors
+
+Right-hand rule for axes - $z$ is up or out of page.
+
+## Angle between vector and axis
+
+Direction of a vector can be given by the angles it makes with $\vec{i}, \vec{j}, \vec{k}$ directions.
+
+For $\vec{a} = a_1 \vec{i} + a_2 \vec{j} + a_3 \vec{k}$ which makes angles $\alpha, \beta, \gamma$ with positive direction of $x, y, z$ axes:
+$$\cos \alpha = {a_1 \over |\vec{a}|}, \quad \cos \beta = {a_2 \over |\vec{a}|}, \quad \cos \gamma = {a_3 \over |\vec{a}|}$$
+