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math:vectors [2021/03/18 02:47] – updated with more info from unit epixmath:vectors [2021/03/18 02:56] (current) – added a note on graphing vectors epix
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 ====== Vectors ====== ====== Vectors ======
-Vectors are line segments that represent the magnitude and direction of a quantity, which is useful for real life quantities like force and velocity. It is usually described by two points/ordered pairs. Vectors are written with an arrow on top of the two point letters instead of a line like for line segments.+Vectors are line segments that represent the magnitude and direction of a quantity, which is useful for real life quantities like force and velocity. It is usually described by two points/ordered pairs. Vectors are written with an arrow on top of the two point letters instead of a line like for line segments. Sometimes it may be useful to graph two vectors as the sum of their parts. Doing this allows you to do trigonometry to find values of the combined vector on harder problems without the hassle of vector math. Trigonometry is also indefinitely useful for this unit. 
 ===== Component Form ===== ===== Component Form =====
 The component form of a vector is the individual changes in horizontal and vertical units that make up the combined vector's magnitude and direction. If the vector is graphed, just //count the boxes™//, otherwise do $y_2 - y_1$ and $x_2 - x_1$ with the ordered pairs they give you for each component. Component form is written with angled brackets (e.g. <2,-1>) to distinguish it from standard ordered pairs. The component form of a vector is the individual changes in horizontal and vertical units that make up the combined vector's magnitude and direction. If the vector is graphed, just //count the boxes™//, otherwise do $y_2 - y_1$ and $x_2 - x_1$ with the ordered pairs they give you for each component. Component form is written with angled brackets (e.g. <2,-1>) to distinguish it from standard ordered pairs.
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 As these are the the base horizontal and vertical component forms, they can be added together to make any integer vector. For example, <3,2> can be written as 3i + 2j. Sometimes vectors are given to you in terms of **i** and **j**. To add these types of vectors together, just substitute them with **i** and **j** and simplify via algebra. As these are the the base horizontal and vertical component forms, they can be added together to make any integer vector. For example, <3,2> can be written as 3i + 2j. Sometimes vectors are given to you in terms of **i** and **j**. To add these types of vectors together, just substitute them with **i** and **j** and simplify via algebra.
  
-==== Parallel or Orthogonal ====+===== Parallel or Orthogonal =====
 Parallel vectors are vector with the same direction but varying magnitude. Check if dividing the two vector's component values give the same ratio for each to see if it is parallel or not. Orthogonal vectors are vectors with a 90 degree angle between them. To check if two vectors are orthogonal, check if their **dot product** equals zero, if so it is orthogonal. Parallel vectors are vector with the same direction but varying magnitude. Check if dividing the two vector's component values give the same ratio for each to see if it is parallel or not. Orthogonal vectors are vectors with a 90 degree angle between them. To check if two vectors are orthogonal, check if their **dot product** equals zero, if so it is orthogonal.

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