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Wiki/Math/Vector Basics.md

@@ -1,13 +1,23 @@
 #rs/class/math163 #math 
 - - -
 ## Operations
-### Projection
+
-$$proj_{u}v=\frac{u\cdot v}{\left|\left|u\right|\right|^{2}}u$$
+### Addition
-Used to project vector $v$ onto $u$
+$$\vec{u} + \vec{v} = <u_{1} + v_{1}, u_{2} + v_{2}>$$
-![[VectorProjection.excalidraw]]
+
+### Subtraction
+$$\vec{u} - \vec{v} = <u_{1} - v_{1}, u_{2} - v_{2}>$$
+
+### Dot Product
+$$\vec{u} \cdot \vec{v} = <u_{1}v_{1}, u_{2}v_{2}>$$
+
+### Magnitude
+$$||\vec{u}|| = \sqrt{ u_{1}^2 + u_{2}^2}$$
+
 ### Unit Vector
-$$ unit_u=\frac{u}{||u||}$$
+$$ unit_u=\frac{\vec{u}}{||\vec{u}||}$$
 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).
@@ -18,6 +28,11 @@ Properties:
 - 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 area of the parallelogram formed with two adjacent sides as the vectors.
+
+### Projection
+$$proj_{u}v=\frac{u\cdot v}{\left|\left|u\right|\right|^{2}}u$$
+Used to project vector $v$ onto $u$
+![[VectorProjection.excalidraw]]
 ### Triple Scalar Product
 Find the Determinant of:
 $$u * (v \times w) = \begin{vmatrix} u_{1} && u_{2} && u_{3} \\ u_{1} && u_{2} && u_{3} \\ u_{1} && u_{2} && u_{3} \end{vmatrix}$$