last attempt (fr): adding space before and after $$ in bullet point

Affected files:
.obsidian/workspace.json
Mathematics/Linear Algebra/Vectors 1.md
Mathematics/Linear Algebra/Vectors.md

.obsidian/workspace.json

@@ -203,11 +203,12 @@
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@@ -222,7 +223,6 @@
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Mathematics/Linear Algebra/Vectors 1.md

@@ -0,0 +1,58 @@
+#math #linear-algebra 
+
+sources:
+[khan academy: Unit 1: Vectors and spaces](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces)
+
+# Vector Definition
+
+It is something that has a magnitude and a direction.
+
+Intuitive example ([source](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/vector-introduction-linear-algebra)):
+
+![](Attachments%20-%20Vectors/Pasted%20image%2020231104130417.png)
+
+# Vector Notation
+
+It has notation like the following: 
+
+$$\vec{v}=\left(5,0\right)=\left[\begin{array}{l}{5}\cr{0}\end{array}\right]=5i+0j$$
+
+Such that:
+* $5$ and $0$ are called ***components*** of a vector, while $(5,0)$ is called a ***2-tuple*** in a 2-D real coordinate space $\left(\mathbb{R}^2\right)$ ([source](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/real-coordinate-spaces)).
+	* Side note 1: $\mathbb{R}^2$ is also called a ***set***, such that $\vec{v}\in\mathbb{R}^2$ is called " vector $\vec{v}$  belongs in the set $\mathbb{R}^2$ "
+* It can also be represented using unit vectors $i$ and $j$ , as explained in the [Unit vector](#Unit%20Vector) section.
+* It can be [added](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/adding-vectors) and [multiplied (by scalers)](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/multiplying-vector-by-scalar)
+
+
+## Vector Addition
+
+Addition visualization ([interactive source](https://sciencepickleapps.com/VisuallyAddingVectorsV1-0-0/), from [this](https://sciencepickle.com/earth-systems/vectors-and-forces/adding-vectors/)):
+![vector-addition](Attachments%20-%20Vectors/vector-addition.mp4)
+
+Example: 
+
+$$\vec{v}=\vec{red}+\vec{green}+\vec{blue}=\left[\begin{array}{c}{-9}\cr{3}\end{array}\right]+\left[\begin{array}{c}{2}\cr{3}\end{array}\right]+\left[\begin{array}{c}{2}\cr{0.2}\end{array}\right]=\left[\begin{array}{c}{-5}\cr{6.2}\end{array}\right]$$
+
+
+## Vector Multiplication
+
+Multiplication visualization ([source](https://makeagif.com/gif/vector-multiplication-by-scalar-G4qCVh)):
+![vector-scalar-multiplication](Attachments%20-%20Vectors/vector-scalar-multiplication.gif)
+
+Formula of a scalar-multiplied vector's magnitude: $||c\cdot \vec v||=|c|\cdot ||\vec v||$ 
+
+To get the reverse direction of a vector, add 180 to its direction.
+
+Example ([source](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/e/scaling_vectors)):
+
+![](Attachments%20-%20Vectors/Pasted%20image%2020231104110053.png)
+
+Answer:
+
+![](Attachments%20-%20Vectors/Pasted%20image%2020231104112518.png)
+
+![](Attachments%20-%20Vectors/Pasted%20image%2020231104112617.png)
+
+
+## Unit Vector
+

Mathematics/Linear Algebra/Vectors.md

@@ -5,22 +5,21 @@ sources:
 
 # Vector Definition
 
-It is something that has a magnitude and a direction.
-
-Intuitive example ([source](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/vector-introduction-linear-algebra)):
-
-![](Attachments%20-%20Vectors/Pasted%20image%2020231104130417.png)
+* It is something that has a magnitude and a direction.
+* Intuitive example ([source](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/vector-introduction-linear-algebra)):
+
+  ![](Attachments%20-%20Vectors/Pasted%20image%2020231104130417.png)
 
 # Vector Notation
 
-It has notation like the following: 
-
-$$\vec{v}=\left(5,0\right)=\left[\begin{array}{l}{5}\cr{0}\end{array}\right]=5i+0j$$
-
-Such that:
-* $5$ and $0$ are called ***components*** of a vector, while $(5,0)$ is called a ***2-tuple*** in a 2-D real coordinate space $\left(\mathbb{R}^2\right)$ ([source](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/real-coordinate-spaces)).
-	* Side note 1: $\mathbb{R}^2$ is also called a ***set***, such that $\vec{v}\in\mathbb{R}^2$ is called " vector $\vec{v}$  belongs in the set $\mathbb{R}^2$ "
-* It can also be represented using unit vectors $i$ and $j$ , as explained in the [Unit vector](#Unit%20Vector) section.
+* It has the following notation: 
+  
+  $$\vec{v}=\left(5,0\right)=\left[\begin{array}{l}{5}\cr{0}\end{array}\right]$$
+  
+	* s
+	* $5$ and $0$ are called ***components*** of a vector, while $(5,0)$ is called a ***2-tuple*** in a 2-D real coordinate space $\left(\mathbb{R}^2\right)$ ([source](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/real-coordinate-spaces)).
+		* Side note 1: $\mathbb{R}^2$ is also called a ***set***, such that $\vec{v}\in\mathbb{R}^2$ is called " vector $\vec{v}$  belongs in the set $\mathbb{R}^2$ "
+		* Side note 2: it can also be represented using unit vectors $i$ and $j$ , as explained in the [Unit vector](#Unit%20vector) section.
 * It can be [added](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/adding-vectors) and [multiplied (by scalers)](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/multiplying-vector-by-scalar)
 
 
@@ -29,8 +28,7 @@ Such that:
 Addition visualization ([interactive source](https://sciencepickleapps.com/VisuallyAddingVectorsV1-0-0/), from [this](https://sciencepickle.com/earth-systems/vectors-and-forces/adding-vectors/)):
 ![vector-addition](Attachments%20-%20Vectors/vector-addition.mp4)
 
-Example: 
-$$\vec{v}=\vec{red}+\vec{green}+\vec{blue}=\left[\begin{array}{c}{-9}\cr{3}\end{array}\right]+\left[\begin{array}{c}{2}\cr{3}\end{array}\right]+\left[\begin{array}{c}{2}\cr{0.2}\end{array}\right]=\left[\begin{array}{c}{-5}\cr{6.2}\end{array}\right]$$
+Example: $\vec{v}=\vec{red}+\vec{green}+\vec{blue}=\left[\begin{array}{c}{-9}\cr{3}\end{array}\right]+\left[\begin{array}{c}{2}\cr{3}\end{array}\right]+\left[\begin{array}{c}{2}\cr{0.2}\end{array}\right]=\left[\begin{array}{c}{-5}\cr{6.2}\end{array}\right]$
 
 ## Vector Multiplication
 
@@ -42,14 +40,11 @@ Formula of a scalar-multiplied vector's magnitude: $||c\cdot \vec v||=|c|\cdot |
 To get the reverse direction of a vector, add 180 to its direction.
 
 Example ([source](https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/e/scaling_vectors)):
-
 ![](Attachments%20-%20Vectors/Pasted%20image%2020231104110053.png)
 Answer:
-
 ![](Attachments%20-%20Vectors/Pasted%20image%2020231104112518.png)
-
 ![](Attachments%20-%20Vectors/Pasted%20image%2020231104112617.png)
 
 
-## Unit Vector
+## Unit vector