Vectors By Scott Forbes

Vectors  Definition of a Vector Definition of a Vector  Addition Addition  Multiplication Multiplication  Unit Vector Unit Vector  Zero Vector Zero Vector  Theorems Theorems  Laws Laws  References References

Definition of a Vector  Point of Application - A vector is a visual representation of a force. The force needs to have a point on which it is being applied.  Direction - A vector must have a specific direction defined by either coordinates, or degrees.  Magnitude - The vector must have length, or magnitude. Magnitude defines the amount of force applied to the point of application. Home

Addition  Tip-to-tail - Adding by connecting the tip of vector A to the tail of vector B. Then draw a new vector from the tail of vector A to the tip of vector B, and that is the sum of the two vectors. Click here for a visual representation.here Home

Tip-to-Tail Home

Multiplication  Dot Product - Multiply the corresponding components of vectors A and B. For example vector A = [ 3,2 ], vector B = [ 4,7 ]. A B = (3 x 4) + (2 x 7) = 26  Cross Product - Set up vectors in cross product form.cross product form  Scalar Home

Cross Product Home

Unit Vector  A unit vector is denoted as a “hatted” letter. An example, â.  Converting using the norm - To convert a vector into a unit vector, divide by the normal vector. Home = normal vector = unit vector

Zero Vector  Has no magnitude  Has no direction  All components are equal to zero Home

Theorems  Two vectors are equivalent if they have the same direction and magnitude.  If a vector, denoted by A, has the same magnitude but opposite direction as vector B, then vector B can be shown as -A. Home

Laws  Addition - Commutative law: A+B = B+A - Associative law: A+(B+C) = (A+B)+C  Multiplication - mA = Am - (m+n)A = mA + nA m and n are different scalar quantities Home

References  Home