184_notes:math_review

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision		 Previous revision
184_notes:math_review [2018/05/17 13:36] – [Unit Vectors] curdemma184_notes:math_review [2020/08/24 19:30] (current) – dmcpadden
Line 1: Line 1:
-[[184_notes:defining_a_system|Next Page: Defining a System]]+/*[[184_notes:defining_a_system|Next Page: Defining a System]]*/
  
 ===== Math Review ===== ===== Math Review =====
Line 50: Line 50:
 →a=|→a|ˆa
 →a=|→a|ˆa
  
-We also use unit vectors to describe the x, y, and z coordinate directions. These are represented by an ˆx, ˆy, and ˆz or by an ˆi, ˆj, and ˆk. Using these coordinate unit vector, you can write any vector in terms of its components. These are common alternative ways to write vectors (as opposed to the bracket notation).+We also use unit vectors to describe the x, y, and z coordinate directions. These are represented by an ˆx, ˆy, and ˆz or by an ˆi, ˆj, and ˆk. Using these coordinate unit vectors, you can write any vector in terms of its components. These are common alternative ways to write vectors (as opposed to the bracket notation).
 →a=axˆx+ayˆy+azˆz
 →a=axˆx+ayˆy+azˆz
 →a=axˆi+ayˆj+azˆk
 →a=axˆi+ayˆj+azˆk
  
 ==== Vector Addition ==== ==== Vector Addition ====
 +[{{  course_planning:course_notes:2d_vector_addition.png?225|graphical vector addition  }}] 
 +[{{ course_planning:course_notes:2d_vector_subtraction.png?225|graphical vector subtraction }}]
 +
  
-{{ course_planning:course_notes:2d_vector_addition.png?250|graphical vector addition}} 
-{{ course_planning:course_notes:2d_vector_subtraction.png?225|graphical vector subtraction}} 
 Two vectors are added (or subtracted) component by component: Two vectors are added (or subtracted) component by component:
 →a+→b=⟨ax,ay,az⟩+⟨bx,by,bz⟩=⟨ax+bx,ay+by,az+bz⟩
 →a+→b=⟨ax,ay,az⟩+⟨bx,by,bz⟩=⟨ax+bx,ay+by,az+bz⟩
 →a−→b=⟨ax,ay,az⟩−⟨bx,by,bz⟩=⟨ax−bx,ay−by,az−bz⟩
 		 →a−→b=⟨ax,ay,az⟩−⟨bx,by,bz⟩=⟨ax−bx,ay−by,az−bz⟩
 
-//**Note: You CANNOT simply add or subtract the magnitudes.**// This disregards the direction that the vectors point in. Alternatively, you can use the [[183_notes:scalars_and_vectors#adding_&_subtracting_vectors|"tip-to-tail" method]] to add or subtract vectors if you have them drawn out graphically. +//**Note: You CANNOT simply add or subtract the magnitudes.**// This disregards the direction that the vectors point in. Alternatively, you can use the [[183_notes:scalars_and_vectors#adding_&_subtracting_vectors|"tip-to-tail" method]] to add or subtract vectors if you have them drawn out graphically. 
 ==== Vector Multiplication ==== ==== Vector Multiplication ====
  
Line 76: Line 76:
  
 There are a couple of ways to calculate the dot product: There are a couple of ways to calculate the dot product:
-{{ 184_notes:dotproducta.png?125|A dot product multiplies the parallel parts of two vectors using the angle between them.}} +[{{ 184_notes:dotproducta.png?125|A dot product multiplies the parallel parts of two vectors using the angle between them.}}] 
-{{ 184_notes:dotproductb.png?150|A dot product multiplies the parallel parts of two vectors using the angle between them.}}+[{{ 184_notes:dotproductb.png?150|A dot product multiplies the parallel parts of two vectors using the angle between them.}}]
  
 - **Using vector components** - If you have two vectors given by →a=⟨ax,ay,az⟩ and →b=⟨bx,by,bz⟩, then you can calculate the dot product by multiplying each component together and adding them together: - **Using vector components** - If you have two vectors given by →a=⟨ax,ay,az⟩ and →b=⟨bx,by,bz⟩, then you can calculate the dot product by multiplying each component together and adding them together:
Line 85: Line 85:
  
 === Cross Product === === Cross Product ===
-{{ 184_notes:crossproducta.png?125|A cross product multiplies the perpendicular parts of two vectors using the angle between them.}} +[{{ 184_notes:crossproducta.png?125|A cross product multiplies the perpendicular parts of two vectors using the angle between them.}}] 
-{{ 184_notes:crossproductb.png?125|A cross product multiplies the perpendicular parts of two vectors using the angle between them.}}+[{{ 184_notes:crossproductb.png?125|A cross product multiplies the perpendicular parts of two vectors using the angle between them.}}]
  
 The cross product is another way to "multiply" two vectors together, which again has some important features: The cross product is another way to "multiply" two vectors together, which again has some important features:
  • 184_notes/math_review.1526564190.txt.gz
  • Last modified: 2018/05/17 13:36
  • by curdemma