Basics of vectors - calculus, Mathematics

Assignment Help:

Vectors - The Basics

Let us start this section off with a quick discussion on what is the use of vector.  Vectors are utilized to present quantities that have both a magnitude and a direction.  Good instances of quantities that can be presented by vectors are force and velocity.  Both of these consist of a direction and a magnitude.  

 Let us consider force for a second.  A force of like 5 Newtons that is applied in a specific direction can be applied at any point in space.  Alternatively, the point where we apply the force does not alter the force itself.  Forces are not dependent of the point of application.  To describe a force all we need to know is the magnitude of the force and the direction which the force is applied in.

 Similar idea holds more usually with vectors.  Vectors just only impart magnitude and direction. 

They don't impart any type of information about where the quantity is applied.  This is an significant idea to all time remember in the study of vectors.

Graphically vectors are presented by directed line segments.  The direction of the line segment is the direction of the vector and length of the line segment is the magnitude of the vector.  Though, because vectors don't impart any information about where the quantity is applied any directed line segment along with similar length and direction will represent similar vector.

Consider the sketch below.  

1945_Basics of Vectors - Calculus 1.png

Every directed line segments in the sketch represents similar vector.  In each case the vector starts at a particular point after that moves 2 units to the left and 5 units up. The notation that we'll make use for this vector is,

1137_Basics of Vectors - Calculus 2.png

and each directed line segments in the diagram are called representations of the vector.


Related Discussions:- Basics of vectors - calculus

How to solve two-step equations, How to solve Two-Step Equations? Two-s...

How to solve Two-Step Equations? Two-step equations involve two math operations - one operation is addition or subtraction. The second operation is multiplication or division.

Function, f(x)=x^2-5x+6, determine inverse of f(x)!

f(x)=x^2-5x+6, determine inverse of f(x)!

Problem of purchasing, story of faicing problem when customer purchasing a ...

story of faicing problem when customer purchasing a product

Brian 100-yard dash time was 2.68 what is the school record, Brian's 100-ya...

Brian's 100-yard dash time was 2.68 seconds more than one school record. Brian's time was 13.4 seconds. What is the school record? The school record is less than Brian's time.

Circles, Circles In this section we are going to take a rapid look at ...

Circles In this section we are going to take a rapid look at circles.  Though, prior to we do that we have to give a quick formula that expectantly you'll recall seeing at som

Relations, Suppose A and B be two non-empty sets then every subset of A Χ B...

Suppose A and B be two non-empty sets then every subset of A Χ B describes a relation from A to B and each relation from A to B is subset of AΧB. Normal 0 fals

Surds, I wanted to know what are surds.please explain with an example.

I wanted to know what are surds.please explain with an example.

Is this a sample statistic.., jenna asked 100 of her schoolmates if they ha...

jenna asked 100 of her schoolmates if they have had their first kiss and 43 of them said yes

#title.heat loss in a cylindrical pipe., briefly explain how the famous equ...

briefly explain how the famous equation for the loss of heat in a cylindrical pipe is derived

What is place value?, WHAT IS PLACE VALUE? : (This section is only for you...

WHAT IS PLACE VALUE? : (This section is only for your assumptions, and not-meant to be passed on to your learners.) You may have realised that in the decimal system the numeral

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd