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.

fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.

Tarell

what is the actual application of fullerenes nowadays?

Damian

That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.

Tarell

what is the Synthesis, properties,and applications of carbon nano chemistry

Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.

Harper

Do you know which machine is used to that process?