Browse Definitions :
Definition

dot product (scalar product)

The dot product, also called the scalar product, of two vector s is a number ( scalar quantity) obtained by performing a specific operation on the vector components. The dot product has meaning only for pairs of vectors having the same number of dimensions. The symbol for dot product is a heavy dot ( ).

In the two-dimensional Cartesian plane, vectors are expressed in terms of the x -coordinates and y -coordinates of their end points, assuming they begin at the origin ( x , y ) = (0,0). Some examples are shown in the illustration below.

The dot product of two vectors is determined by multiplying their x -coordinates, then multiplying their y -coordinates, and finally adding the two products. Thus, in the above example:

A B = (2 x -4) + (5 x -3) = -8 - 15 = -23

B C = (-4 x 5) + (-3 x -5) = -20 + 15 = -5

C A = (5 x 2) + (-5 x 5) = 10 - 25 = -15

In polar coordinates, vectors are expressed in terms of length (magnitude) and direction. When expressed in this format, the dot product of two vectors is equal to the product of their lengths, multiplied by the cosine of the angle between them.

For any two vectors A and B , A B = B A . That is, the dot product operation is commutative; it does not matter in which order the operation is performed.

Also see Fast Reference for Math Symbols .

This was last updated in March 2011

Join the conversation

1 comment

Send me notifications when other members comment.

Please create a username to comment.

this answer is not up to my mark
Cancel

-ADS BY GOOGLE

File Extensions and File Formats

SearchCompliance

  • risk management

    Risk management is the process of identifying, assessing and controlling threats to an organization's capital and earnings.

  • compliance as a service (CaaS)

    Compliance as a Service (CaaS) is a cloud service service level agreement (SLA) that specified how a managed service provider (...

  • data protection impact assessment (DPIA)

    A data protection impact assessment (DPIA) is a process designed to help organizations determine how data processing systems, ...

SearchSecurity

  • cybersecurity insurance (cybersecurity liability insurance)

    Cybersecurity insurance, also called cyber liability insurance or cyber insurance, is a contract that an entity can purchase to ...

  • phishing

    Phishing is a form of fraud in which an attacker masquerades as a reputable entity or person in email or other communication ...

  • cybercrime

    Cybercrime is any criminal activity that involves a computer, networked device or a network.

SearchHealthIT

SearchDisasterRecovery

  • business continuity plan (BCP)

    A business continuity plan (BCP) is a document that consists of the critical information an organization needs to continue ...

  • disaster recovery team

    A disaster recovery team is a group of individuals focused on planning, implementing, maintaining, auditing and testing an ...

  • cloud insurance

    Cloud insurance is any type of financial or data protection obtained by a cloud service provider. 

SearchStorage

  • NVMe over Fabrics (NVMe-oF)

    NVMe over Fabrics, also known as NVMe-oF and non-volatile memory express over fabrics, is a protocol specification designed to ...

  • logical unit number (LUN)

    A logical unit number (LUN) is a unique identifier for designating an individual or collection of physical or virtual storage ...

  • CIFS (Common Internet File System)

    CIFS (Common Internet File System) is a protocol that gained popularity around the year 2000, as vendors worked to establish an ...

Close