Understand the rules of vector addition, subtraction, and multiplication.

Apply graphical methods of vector addition and subtraction to determine the displacement of moving objects.

Vectors in two dimensions

A
vector is a quantity that has magnitude and direction. Displacement, velocity, acceleration, and force, for example, are all vectors. In one-dimensional, or straight-line, motion, the direction of a vector can be given simply by a plus or minus sign. In two dimensions (2-d), however, we specify the direction of a vector relative to some reference frame (i.e., coordinate system), using an arrow having length proportional to the vector’s magnitude and pointing in the direction of the vector.

[link] shows such a
graphical representation of a vector , using as an example the total displacement for the person walking in a city considered in
Kinematics in Two Dimensions: An Introduction . We shall use the notation that a boldface symbol, such as
$\text{D}$ , stands for a vector. Its magnitude is represented by the symbol in italics,
$D$ , and its direction by
$\theta $ .

Vectors in this text

In this text, we will represent a vector with a boldface variable. For example, we will represent the quantity force with the vector
$\text{F}$ , which has both magnitude and direction. The magnitude of the vector will be represented by a variable in italics, such as
$F$ , and the direction of the variable will be given by an angle
$\theta $ .

Vector addition: head-to-tail method

The
head-to-tail method is a graphical way to add vectors, described in
[link] below and in the steps following. The
tail of the vector is the starting point of the vector, and the
head (or tip) of a vector is the final, pointed end of the arrow.

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387

In this morden time nanotechnology used in many field .
1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc
2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc
3- Atomobile -MEMS, Coating on car etc.
and may other field for details you can check at Google

Azam

anybody can imagine what will be happen after 100 years from now in nano tech world

Prasenjit

after 100 year this will be not nanotechnology maybe this technology name will be change .
maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments

Azam

name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world

Prasenjit

how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?

Damian

silver nanoparticles could handle the job?

Damian

not now but maybe in future only AgNP maybe any other nanomaterials

Azam

Hello

Uday

I'm interested in Nanotube

Uday

this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15

Prasenjit

can nanotechnology change the direction of the face of the world

At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.