Vector Solutions, Shortcuts, Formulas
Section Formula
Let P and Q be two points represented by the position vectors OP and OQ , respectively, with respect to the origin O. Then the line segment joining the points P and Q may be divided by a third point, say R, in two ways – internally (Fig 10.16) and externally (Fig 10.17). Here, we intend to find the position vector OR for the point R with respect to the origin O .we take the two cases ;
Case I) where R divided PQ internally . where m and n point R divides PQ internally in the ratio of m : n . Now from triangles ORQ and OPR, we have,
Hence , the position vector of the point R which divides P and Q internally in the ratio of m: n is given b
Case II) When R divides PQ externally (Fig 10.17). We leave it to the reader as an exercise to verify
that the position vector of the point R which divides the line segment PQ externally in the ratio m : n , i.e
Product of two vector : other algebraic operation which we intend to discuss regarding vectors is their product. We may recall that product of two numbers is a number, product of two matrices is again a matrix. But in case of functions, we may multiply them in two ways, namely, multiplication of two functions point wise and composition of two functions. Similarly, multiplication of two vectors is also defined in two ways, namely, scalar (or dot) product where the result is a scalar, and vector (or cross) product where the result is a vector. Based upon these two types of products for vectors, they have found various applications in geometry, mechanics and engineering. In this section, we will discuss these two types of products.
Scalar (or dot ) product of two vector :The scalar product of of two non zero vector a and vector b , denoted by vector is define as
where, θ is the angle between and , 0 is not defined, and in this case
Latest Jobs

 Type
 Job Notification
 Job
 Indian Institute of Technology Hyderabad Recruitment of 152 JE, Engineer, Library Assistant, MTS  Last Date 17022020
 Location
 HyderabadTelangana, India
 Date Posted
 6 Feb 2020

 Type
 Job Notification
 Job
 SBI Recruitment of 100 Specialist Officers  Last Date 12022020
 Location
 Anywhere
 Date Posted
 4 Feb 2020

 Type
 Job Notification
 Job
 INDIAN Bank Recruitment 138 Specialist Officers  Last Date  10022020
 Location
 Anywhere
 Date Posted
 3 Feb 2020

 Type
 Job Notification
 Job
 KVIC Recruitment of 108 GroupB and GroupC categories  Last Date 19012020
 Location
 MumbaiMaharashtra, India
 Date Posted
 7 Jan 2020

 Type
 Job Notification
 Job
 SAIL Durgapur Steel Plant Recruitment of Manager, Technician, Medical Service Provider  27012020
 Location
 DurgapurWest Bengal, India
 Date Posted
 7 Jan 2020

 Type
 Job Notification
 Job
 Indian Coast Guard Recruitment 260 Navik  Last Date 02022020
 Location
 Anywhere
 Date Posted
 7 Jan 2020

 Type
 Job Notification
 Job
 IOCL hiring 312 Apprentices  Last Date 22012020
 Location
 Anywhere
 Date Posted
 7 Jan 2020

 Type
 Job Notification
 Job
 RBI Recruitment NEWS for 926 Assistants  Last Date 16012020
 Location
 Anywhere
 Date Posted
 7 Jan 2020

 Type
 Job Notification
 Job
 Janki Devi Memorial College Recruitment 71 Assistant Professor  Last Date 04012020
 Location
 DelhiDelhi, India
 Date Posted
 2 Jan 2020

 Type
 Job Notification
 Job
 NPCIL Recruitment of Trainee, Electrician, Fitter, Machinist, Welder, Driver  Last Date 21012020
 Location
 RawatbhataRajasthan, India
 Date Posted
 2 Jan 2020