184_notes:math_review

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184_notes:math_review [2018/05/17 13:43] – [Vector Addition] curdemma184_notes:math_review [2018/05/17 13:47] – [Vector Multiplication] curdemma
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 ==== Vector Addition ==== ==== Vector Addition ====
  
-[{{  course_planning:course_notes:2d_vector_addition.png?225|graphical vector addition}}]  +[{{  course_planning:course_notes:2d_vector_addition.png?200|graphical vector addition}}] 
-[{{  course_planning:course_notes:2d_vector_subtraction.png?225|graphical vector subtraction}}]+[{{  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:
 $$ \vec{a} +\vec{b} = \langle a_x, a_y, a_z \rangle + \langle b_x, b_y, b_z \rangle = \langle a_x+b_x, a_y+b_y, a_z+b_z \rangle  $$ $$ \vec{a} +\vec{b} = \langle a_x, a_y, a_z \rangle + \langle b_x, b_y, b_z \rangle = \langle a_x+b_x, a_y+b_y, a_z+b_z \rangle  $$
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 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 $\vec{a}=\langle a_x, a_y, a_z \rangle$ 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