ÔN TẬP
CHƯƠNG III

ÔN TẬP CHƯƠNG III
BÀI 1: PHƯƠNG PHÁP TỌA ĐỘ
TRONG KHÔNG GIAN
I. HỆ THỐNG LẠI KIẾN THỨC
II. LUYỆN TẬP

I. Hệ thống lại kiến thức
H1: Trong không gian cho các véctơ, Tính , , , (k là một số thực).
Giải
H1:

.

H2: Trong không gian nếu cho hai điểm Tính ính tọa độ trung điểm của đoạn thẳng
AB.
Giải
là:
H3: Viết phương trình của mặt cầu khi biết tâm (a;b;c) và bán kính R.
Giải
Mặt cầu tâm , bán kính có phương trình:
Phương trình mặt cầu nói trên có thể viết dưới dạng:
với

II. LUYỆN TẬP
Bài 1: Cho ba vecto
a) Tính tọa độ của vecto
b) Tính tọa độ của vecto
Giải
Bài 1:a) Ta có
Suy ra
b) Ta có:
Vậy

Bài 2: Tính:
a) với
b)

Giải
a)

Bài 3: ( trang 91 SGK) Trong không gian cho mặt cầu có
đường kính biết rằng .
a) Tìm toạ độ tâm và tính bán kính của mặt cầu .
b) Lập phương trình mặt cầu
Giải
Bài 3:
a) Vì I là trung điểm AB nên ta có: .
b) Phương trình mặt cầu

BÀI TẬP TRẮC NGHIỆM
Trong không gian cho ba vecto , .
Sử dụng giả thiết này để trả lời các câu hỏi 1, 2 và 3 sau đây:
1. Trong các mệnh đề sau, mệnh đề nào sai?
A.
B.
C. ;
D.
2. Trong các mệnh đề sau, mệnh đề nào đúng?
A. ;
B. cùng phương;
C.
D. .
3. Cho hình bình hành OADB có (O là gốc tọa độ). Tọa độ tâm hình bình hành OADB
là:
A.
B.
C.
D. .
4. Trong không gian với hệ tọa độ Oxyz, cho mặt cầu
. Tâm của mặt cầu (S) là:
A.
B.
C.
D. .
5. Trong không gian với hệ trục tọa độ , mặt cầu tâm đi qua điểm có phương trình
A.
B.
C.
D. .

Bài 4: Biết phương trình mặt cầu có tâm và cắt đường thẳng tại hai điểm với .

Bài 4: Biết phương trình mặt cầu có tâm và cắt đường thẳng tại hai điểm với .

Giải
Gọi H là hình chiếu vuông góc của I trên đường thẳng d.
Vì H thuộc d nên Suy ra
Đường thẳng d có vectơ chỉ phương là
Vì IH vuông góc với đường thẳng d nên
Suy ra nên
Vì nên 
Áp dụng định lí Py – ta – go trong tam giác vuông ta có:
Vậy bán kính mặt cầu là
Khi đó phương trình mặt cầu là:

01
Objectives
of the project

Objectives

Our aim

The goal

An aim in a corporate context is a
goal or desired result that the
organization seeks to achieve. The
aim should be clear and achievable,
and often serves as the basis for
further planning actions inside the
organization

Goals inside a company are usually
specific and measurable, with
clearly defined deadlines and
outcomes. The company's goals
help focus the actions of the
organization and ensure resources
are used effectively

Resources
Human resources
The project team is responsible for the successful execution of the
project. Our team is composed of experienced professionals with the
necessary skills and expertise to complete the project on time and within
budget

Financial resources
Our project budget is $100,000. This budget includes all expenses
associated with the project, including salaries and equipment. We have
allocated these resources to ensure that we are able to complete the
project within budget

Physical resources
Our project requires a number of specialized pieces of equipment. We will
be using [insert equipment and their functions]. All equipment is in good
working condition and has been tested and calibrated prior to use

Budget
Sources of funding

Personnel costs

Funding for a company can come from
personal savings or investments, bank loans
and other loan options, venture capital and
angel investors, grants, competitions or
programs, crowdfunding…

Personnel costs refer to the expenses incurred
in hiring, training and retaining staff for a
company. This can include salaries, bonuses,
benefits and other payroll-related costs

Equipment and
materials

Travel and
miscellaneous

Equipment and materials costs refer to all the
expenses related to the purchasing,
maintenance and upkeep of any physical
items used in production or other business
processes inside the company

Travel and miscellaneous costs refer to
expenses related to any travel-related
activities, such as conferences, trainings or
business trips. It may also include office
supplies, communications services, licenses
and other miscellaneous expenses

Solutions
Solution 1

Solution 2

Solution 3

Implementing a new CRM
(Customer Relationship
Management) system to
improve customer data
management and
sales tracking

Outsourcing specific
business functions (such
as accounting or IT) to a
third-party provider to
reduce costs and increase
time efficiency

Launching an e-commerce
platform to expand the
reach of the business and
increase online sales

Solution 4

Solution 5

Solution 6

Developing a new product
or service to diversify the
business and increase
revenue streams

Implementing a costsaving initiative, such as
energy-efficient practices
or process automation, to
reduce expenses

Establishing strategic
partnerships with other
businesses to gain access
to new markets or
innovative technologies

$500,00
0
200
units
25%
Net profit of the project

Break-even point

Market share in the industry

10 million
First-year revenue of the project

Project data
Benefits of
using graphs
Graphs in project
proposals offer visual
organization, enabling
clear presentation of
information in a structured
format. They enhance the
visual appeal, facilitate
data comparison and
improve overall clarity and
professionalism of your
project proposal
Follow the link in the graph to modify its data and then paste the new one here. For more info, click here

Project activities
Activity

Start
date

End date

Resource

Cost

Market
research

1/1/20XX

1/15/20XX

Market
research firm

$20,000

Product
development

1/16/20XX

6/30/20XX

R&D team

$200,000

Beta testing

7/1/20XX

8/15/20XX

Beta testers

$10,000

Marketing
campaign

1/1/20XX

1/15/20XX

Advertising
agency

$100,000

Product
launch

1/16/20XX

6/30/20XX

Sales team

$50,000

$500,000

Post-launch
support

7/1/20XX

8/15/20XX

Support team

$50,000

$800,000

Revenue

What to
show in a
mockup
1.
2.
3.

Product/website description: A brief overview of
the product/website, including its key features,
dimensions, and materials used
Features and benefits: A detailed explanation of
the product's/website's features and how they
will benefit the user
Technical specifications: A list of the
product's/website's technical specifications,
such as dimensions, weight, power
requirements, connectivity options and hosting
platform

Conduct market research and
analyze the target audience to
identify opportunities
Create the product or service
by defining features, design,
and functionality
Test the product with a group
of users to receive feedback
and improve the product
Execute a marketing campaign
to promote the product to the
target audience

Project timeline
0
0
1
8
0
0
2
7
0
0
3
6
0
0
4
5

Continuously improve the
product based on customer
feedback and market trends
Explore opportunities for
growth and expansion of the
product or service

Provide customer support to
ensure customer satisfaction

Release the product or service
to the market with a
comprehensive launch plan

Project roadmap
Initiative

Objective

Market research

Increase brand awareness
by 30% within the first year

Product
development

Achieve a customer
satisfaction rate of 90%

Marketing
campaign

Increase revenue by 20%
within the first year

Product launch

Achieve a customer
satisfaction rate of 90%
within the first year

Expansion

Reduce costs by 15%
within the first year by
expanding the product

Partnership

Reach profitability within
18 months of launch

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Photo showcase
A photo showcase can be a useful addition to a business project
proposal as it can help to visually communicate the concept or idea
being proposed

Project expenses
Labor
Materials
Equipme
nt
Overhead
Other
Follow the link in the graph to modify its data and then paste the new one here. For more info, click here

KPI dashboard

120 u/day

2h

Output per worker

Time to complete a task

Follow the link in the graph to modify its data and then
paste the new one here. For more info, click here

Resource

Utilization
rate

Cost
per unit

Labor

85%

$50

Equipment

70%

$100

Materials

95%

$20

Rent

90%

$1,000

Energy

80%

$80

Software
licenses

80%

$200

Advertising

60%

$500

Thanks!
Do you have any questions?
youremail@freepik.com
+34 654 321 432
yourwebsite.com

CREDITS: This presentation template was created by Slidesgo,
and includes icons by Flaticon, and infographics & images by
Freepik
Please keep this slide for attribution

Alternative resources
Here's an assortment of alternative resources whose style fits that of this template:
Photos
●
●
●
●

Black and golden marble background
Realistic liquid marble background with gold
Watercolor alcohol ink background
Abstract marble black and gold background

Resources
Did you like the resources in this template? Get them on these
websites:
Photos
●
●
●
●
●
●
●
●
●
●
●
●
●

Abstract marble gold background
Abstract marble gold background II
Abstract marble gold background III
Abstract marble gold background IV
Abstract marble gold background V
Abstract marble gold background VI
Abstract marble black and gold background
Black man giving presentation on a meeting
Industrial designers working on 3d model
Industrial designers working on 3d model I
Industrial designers working on 3d model II
Industrial designers working on 3d model III
Industrial designers working on 3d model IV

Instructions for use
If you have a free account, in order to use this template, you must credit Slidesgo by keeping the Thanks slide. Please
refer to the next slide to read the instructions for premium users.
As a Free user, you are allowed to:
●
●

Modify this template.
Use it for both personal and commercial projects.

You are not allowed to:
●
Sublicense, sell or rent any of Slidesgo Content (or a modified version of Slidesgo Content).
●
Distribute Slidesgo Content unless it has been expressly authorized by Slidesgo.
●
Include Slidesgo Content in an online or offline database or file.
●
Offer Slidesgo templates (or modified versions of Slidesgo templates) for download.
●
Acquire the copyright of Slidesgo Content.

For more information about editing slides, please read our FAQs or visit our blog:
https://slidesgo.com/faqs and https://slidesgo.com/slidesgo-school

Instructions for use (premium users)
As a Premium user, you can use this template without attributing Slidesgo or keeping the "Thanks" slide.
You are allowed to:
●
Modify this template.
●
Use it for both personal and commercial purposes.
●
Hide or delete the “Thanks” slide and the mention to Slidesgo in the credits.
●
Share this template in an editable format with people who are not part of your team.
You are not allowed to:
●
Sublicense, sell or rent this Slidesgo Template (or a modified version of this Slidesgo Template).
●
Distribute this Slidesgo Template (or a modified version of this Slidesgo Template) or include it in a database or in
any other product or service that offers downloadable images, icons or presentations that may be subject to
distribution or resale.
●
Use any of the elements that are part of this Slidesgo Template in an isolated and separated way from this
Template.
●
Register any of the elements that are part of this template as a trademark or logo, or register it as a work in an
intellectual property registry or similar.
For more information about editing slides, please read our FAQs or visit our blog:
https://slidesgo.com/faqs and https://slidesgo.com/slidesgo-school

Fonts & colors used
This presentation has been made using the following fonts:
Elsie Swash Caps
(https://fonts.google.com/specimen/Elsie+Swash+Caps)
Questrial
(https://fonts.google.com/specimen/Questrial)

#191919

#ffffff

#fce1b7

#eeeeee

#f1c232

#595959

#e69138

#4b4848

#8f5112

Storyset
Create your Story with our illustrated concepts. Choose the style you like the most, edit its
colors, pick the background and layers you want to show and bring them to life with the
animator panel! It will boost your presentation. Check out how it works.

Pana

Amico

Bro

Rafiki

Cuate

Use our editable graphic resources...
You can easily resize these resources without losing quality. To change the color, just ungroup the resource and click on
the object you want to change. Then, click on the paint bucket and select the color you want. Group the resource again
when you're done. You can also look for more infographics on Slidesgo.

JANUARY

FEBRUARY

MARCH

APRIL

MAY

JUNE

PHASE 1
Task 1
Task 2
PHASE 2
Task 1
Task 2

JANUARY

PHASE 1

Task 1

Task 2

FEBRUARY

MARCH

APRIL

...and our sets of editable icons
You can resize these icons without losing quality.
You can change the stroke and fill color; just select the icon and click on the paint bucket/pen.
In Google Slides, you can also use Flaticon's extension, allowing you to customize and add even more icons.

Educational Icons

Medical Icons

Business Icons

Teamwork Icons

Help & Support Icons

Avatar Icons

Creative Process Icons

Performing Arts Icons

Nature Icons

SEO & Marketing Icons