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
Last revisionBoth sides next revision
184_notes:math_review [2018/05/17 13:47] – [Vector Multiplication] curdemma184_notes:math_review [2018/05/17 13:56] – [Vector Addition] curdemma
Line 55: Line 55:
  
 ==== 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?200|graphical vector addition}}] 
-[{{  course_planning:course_notes:2d_vector_subtraction.png?200|graphical vector subtraction}}] 
 Two vectors are added (or subtracted) component by component: Two vectors are added (or subtracted) component by component:
 $$ \vec{a} +\vec{b} = \langle a_x, a_y, a_z \rangle + \langle b_x, b_y, b_z \rangle = \langle a_x+b_x, a_y+b_y, a_z+b_z \rangle  $$ $$ \vec{a} +\vec{b} = \langle a_x, a_y, a_z \rangle + \langle b_x, b_y, b_z \rangle = \langle a_x+b_x, a_y+b_y, a_z+b_z \rangle  $$
 $$ \vec{a} - \vec{b} = \langle a_x, a_y, a_z \rangle - \langle b_x, b_y, b_z \rangle = \langle a_x-b_x, a_y-b_y, a_z-b_z \rangle $$  $$ \vec{a} - \vec{b} = \langle a_x, a_y, a_z \rangle - \langle b_x, b_y, b_z \rangle = \langle a_x-b_x, a_y-b_y, a_z-b_z \rangle $$ 
-//**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 75: 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:dotproductb.png?150|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.}}]
  
 - **Using vector components** - If you have two vectors given by $\vec{a}=\langle a_x, a_y, a_z \rangle$ and $\vec{b}=\langle b_x, b_y, b_z\rangle$, 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 $\vec{a}=\langle a_x, a_y, a_z \rangle$ and $\vec{b}=\langle b_x, b_y, b_z\rangle$, then you can calculate the dot product by multiplying each component together and adding them together:
  • 184_notes/math_review.txt
  • Last modified: 2020/08/24 19:30
  • by dmcpadden