How to Add or Subtract Vectors

Step-by-Step Guide

1. 1

   Step 1: Express a vector in terms of components in some coordinate system usually x

   These component parts are usually expressed with a notation similar to that used to describe points in a coordinate system (e.g. <x,y,z>
   
   etc.).
   
   If these pieces are known, adding or subtracting vectors is just a simple adding or subtracting the x, y, and z components.
   
   Note that vectors can be 1, 2, or 3-dimensional.
   
   Thus, vectors can have an x component, an x and y component, or an x, y, and z component.
   
   Let's say that we have two 3-dimensional vectors, vector A and vector B.
   
   We might write these vectors in components as A = <Ax,Ay,Az > and B = <Bx,By,Bz>
   
   using x y z components accordingly.
2. 2

   Step 2: and possibly z in usual 2 or 3 dimensional space (higher dimensionality is possible too in some mathematical situations).

   In other words, add the x component of the first vector to the x component of the second and so on for for y and z.
   
   The answers you get from adding the x, y, and z components of your original vectors are the x, y, and z components of your new vector.
   
   In general terms, A+B = <Ax+Bx,Ay+By,Az+Bz>.
   
   Let's add two vectors A and B.
   
   Example:
   A = <5, 9,
   -10> and B = <17,
   -3,
   -2>.
   
   A + B = <5+17, 9+-3,
   -10+-2>
   
   or <22, 6,
   -12>. , Note that subtracting one vector from another A-B can be thought of adding the "reverse" of that second A+(-B)., A = <18, 5, 3> and B = <10, 9,
   -10>.
   
   A
   - B = <18-10, 5-9, 3-(-10)>
   
   or <8,
   -4, 13>.
3. 3

   Step 3: To add two vectors

4. 4

   Step 4: we simply add their components.

5. 5

   Step 5: To subtract two vectors

6. 6

   Step 6: subtract their components.

7. 7

   Step 7: In general terms

8. 8

   Step 8: A-B = <Ax-Bx

9. 9

   Step 9: Az-Bz> Let's subtract two vectors A and B.

Detailed Guide

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