diff --git a/Wiki/Math/Vector Basics.md b/Wiki/Math/Vector Basics.md index bd018be..d96014e 100644 --- a/Wiki/Math/Vector Basics.md +++ b/Wiki/Math/Vector Basics.md @@ -2,4 +2,17 @@ ### Projection $$proj_{u}v=\frac{u\cdot v}{\left|\left|u\right|\right|^{2}}u$$ Used to project vector $v$ onto $u$ -![[VectorProjection.excalidraw]] \ No newline at end of file +![[VectorProjection.excalidraw]] +### Unit Vector +$$ unit_u=\frac{u}{||u||}$$ +Used to find the vector of magnitude 1 in the same direction as $u$ +### Cross Product +$$a \times b = \begin{vmatrix} i&j&k\\a_1&a_2&a_3\\b_1&b_2&b_3\end{vmatrix}= i(a_2b_3-a_3b_2)-j(a_1b_3-a_3b_1)+k(a_1b_2-a_2b_1)$$ +Used to create a vector that is orthogonal to both $a$ and $b$. To find what direction it will point in use the right-hand rule (thumb, pointer and middle finger). + +Properties: +- Not commutative $$u\times v \ne v \times u$$ +- Anti-commutative $$ u \times v = -(v \times u) $$ +- On self $$ a \times a = 0 $$ +The magnitude of the cross product of two vectors can be found with $$||u \times v|| = ||u|| * ||v|| * \sin(\theta)$$ +The magnitude of the cross product is equal to the \ No newline at end of file