# Vectors  (Page 2/10)

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## Bearing

The final method of expressing direction is to use a bearing . A bearing is a direction relative to a fixed point.

Given just an angle, the convention is to define the angle with respect to the North. So, a vector with a direction of $110{}^{\circ }$ has been rotated clockwise $110{}^{\circ }$ relative to the North. A bearing is always written as a three digit number, for example $275{}^{\circ }$ or $080{}^{\circ }$ (for $80{}^{\circ }$ ).

## Scalars and vectors

1. Classify the following quantities as scalars or vectors:
1. 12 km
2. 1 m south
3. $2\phantom{\rule{2pt}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}$ , $45{}^{\circ }$
4. $075{}^{\circ }$ , 2 cm
5. $100\phantom{\rule{2pt}{0ex}}\mathrm{k}·{\mathrm{h}}^{-1}$ , $0{}^{\circ }$
2. Use two different notations to write down the direction of the vector in each of the following diagrams:

## Drawing vectors

In order to draw a vector accurately we must specify a scale and include a reference direction in the diagram. A scale allows us totranslate the length of the arrow into the vector's magnitude. For instance if one chose a scale of 1 cm = 2 N (1 cm represents 2 N), aforce of 20 N towards the East would be represented as an arrow 10 cm long. A reference direction may be a line representing a horizontal surface or the points of a compass.

Method: Drawing Vectors

1. Decide upon a scale and write it down.
2. Determine the length of the arrow representing the vector, by using the scale.
3. Draw the vector as an arrow. Make sure that you fill in the arrow head.
4. Fill in the magnitude of the vector.

Represent the following vector quantities:

1. $6\phantom{\rule{2pt}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}$ north
2. 16 m east
1. $1\phantom{\rule{2pt}{0ex}}\mathrm{cm}=2\phantom{\rule{2pt}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}$
2. $1\phantom{\rule{2pt}{0ex}}\mathrm{cm}=4\phantom{\rule{2pt}{0ex}}\mathrm{m}$
1. If $1\phantom{\rule{2pt}{0ex}}\mathrm{cm}=2\phantom{\rule{2pt}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}$ , then $6\phantom{\rule{2pt}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}=3\phantom{\rule{2pt}{0ex}}\mathrm{cm}$
2. If $1\phantom{\rule{2pt}{0ex}}\mathrm{cm}=4\phantom{\rule{2pt}{0ex}}\mathrm{m}$ , then $16\phantom{\rule{2pt}{0ex}}\mathrm{m}=4\phantom{\rule{2pt}{0ex}}\mathrm{cm}$
1. Scale used: $1\phantom{\rule{2pt}{0ex}}\mathrm{cm}=2\phantom{\rule{2pt}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}$ Direction = North
2. Scale used: $1\phantom{\rule{2pt}{0ex}}\mathrm{cm}=4\phantom{\rule{2pt}{0ex}}\mathrm{m}$ Direction = East

## Drawing vectors

Draw each of the following vectors to scale. Indicate the scale that you have used:

1. 12 km south
2. 1,5 m N $45{}^{\circ }$ W
3. $1\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ , $20{}^{\circ }$ East of North
4. $50\phantom{\rule{2pt}{0ex}}\mathrm{km}·\mathrm{h}{}^{-1}$ , $085{}^{\circ }$
5. 5 mm, $225{}^{\circ }$

## Mathematical properties of vectors

Vectors are mathematical objects and we need to understand the mathematical properties of vectors, like adding and subtracting.

For all the examples in this section, we will use displacement as our vector quantity. Displacement was discussed in Grade 10.

Displacement is defined as the distance together with direction of the straight line joining a final point to an initial point.

Remember that displacement is just one example of a vector. We could just as well have decided to use forces or velocities to illustrate the properties of vectors.

When vectors are added, we need to add both a magnitude and a direction. For example, take 2 steps in the forward direction, stop and then take another 3 steps in the forward direction. The first 2 steps is a displacement vector and the second 3 steps is also a displacement vector. If we did not stop after the first 2 steps, we would have taken 5 steps in the forward direction in total. Therefore, if we add the displacement vectors for 2 steps and 3 steps, we should get a total of 5 steps in the forward direction. Graphically, this can be seen by first following the first vector two steps forward and then following the second one three steps forward (ie. in the same direction):

#### Questions & Answers

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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