Calculus II/Vector Algebra Operation

Definitions of a vector

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A vector is a mathematical concept that has both magnitude and direction. A vector is an object that has certain properties:

  • Magnitude (or length) denoted as A
  • Direction . denoted as a

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A vector   of length X pointing from left to right horizontally

 

A vector   of length X pointing from bottom to top vertically

 

From above, A vector   of length X pointing from left to right horizontally

 
 
 

Addition of 2 vector

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A Vector sum of 2 vectors

 

Example

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Substraction of 2 vector

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A Vector difference of 2 vectors

 

Example

 

Multiplication by a scalar

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Multiplication of a vector   by a scalar   has the effect of stretching or shrinking the vector (see Figure 2(b)).

You can form a unit vector   that is parallel to   by dividing by the length of the vector  . Thus,