Vector Solutions, Shortcuts, Formulas

Position Vector

A vector \vec{AB} simply means the displacement from a point A to the point B. Now consider a situation that a girl moves from A to B and then from B to C (Fig 10.7). The net displacement made by the girl from point A to the point C, is given by the vector \vec{AC} and express \vec{AC}=\vec{AB}+\vec{AC}
This is known as the triangle law of vector addition.

If we have two vectors \vec{a}\: and\: \vec{b} by the two adjacent sides of a parallelogram in magnitude and direction (Fig 10.9), then their sum is represented in magnitude and direction by the diagonal of the parallelogram through their common point. This is known as the parallelogram law of vector addition.
Using triangle law , \vec{OA}+\vec{AC}=\vec{OC}
\vec{OA}+\vec{OB}=\vec{OC} (since \vec{AC}=\vec{OB}
Which is parallelogram law. Thus, we may say that the two laws of vector addition are equivalent to each other

Properties of Vector Addition

1) For any two vector \vec{a}\: and\: \vec{b}
\vec{a}+\vec{b}=\vec{b}+\vec{a} (commutative properties)

2) For any three properties \vec{a},\vec{b}\:and\: \vec{c}
(\vec{a}+\vec{b})+\vec{c}=\vec{a}+(\vec{b}+\vec{c}) (Associative properties )

Note: The associative property of vector addition enables us to write the sum of three vectors \vec{a},\vec{b,\vec{c}}\: as\:\vec{a}+\vec{b}+\vec{c} as without using brackets. Note that for any vector \vec{a} , we have \vec{a}+\vec{0}=\vec{0}+\vec{a}=\vec{a}
Here , the zero vector is called additive identity for the vector addition .

 

Latest Jobs

  1. Type
    Job Notification
    Job
    Indian Institute of Technology Hyderabad Recruitment of 152 JE, Engineer, Library Assistant, MTS - Last Date 17-02-2020
    Location
    HyderabadTelangana, India
    Date Posted
    6 Feb 2020
  2. Type
    Job Notification
    Job
    SBI Recruitment of 100 Specialist Officers - Last Date 12-02-2020
    Location
    Anywhere
    Date Posted
    4 Feb 2020
  3. Type
    Job Notification
    Job
    INDIAN Bank Recruitment 138 Specialist Officers - Last Date - 10-02-2020
    Location
    Anywhere
    Date Posted
    3 Feb 2020
  4. Type
    Job Notification
    Job
    KVIC Recruitment of 108 Group-B and Group-C categories - Last Date 19-01-2020
    Location
    MumbaiMaharashtra, India
    Date Posted
    7 Jan 2020
  5. Type
    Job Notification
    Job
    SAIL Durgapur Steel Plant Recruitment of Manager, Technician, Medical Service Provider - 27-01-2020
    Location
    DurgapurWest Bengal, India
    Date Posted
    7 Jan 2020
  6. Type
    Job Notification
    Job
    Indian Coast Guard Recruitment 260 Navik - Last Date 02-02-2020
    Location
    Anywhere
    Date Posted
    7 Jan 2020
  7. Type
    Job Notification
    Job
    IOCL hiring 312 Apprentices - Last Date 22-01-2020
    Location
    Anywhere
    Date Posted
    7 Jan 2020
  8. Type
    Job Notification
    Job
    RBI Recruitment NEWS for 926 Assistants - Last Date 16-01-2020
    Location
    Anywhere
    Date Posted
    7 Jan 2020
  9. Type
    Job Notification
    Job
    Janki Devi Memorial College Recruitment 71 Assistant Professor - Last Date 04-01-2020
    Location
    DelhiDelhi, India
    Date Posted
    2 Jan 2020
  10. Type
    Job Notification
    Job
    NPCIL Recruitment of Trainee, Electrician, Fitter, Machinist, Welder, Driver - Last Date 21-01-2020
    Location
    RawatbhataRajasthan, India
    Date Posted
    2 Jan 2020

Jobs by Category

Syllabus and Previous Papers

Leave a Reply

Your email address will not be published. Required fields are marked *