Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Two Vectors - Vector Geometry - Exam, Exams of Computational Geometry

This is the Exam of Vector Geometry and its key important points are: Two Vectors, Particular Vectors, Zero Vector, Scalar Multiple, Perpendicular, Line of Intersection, Two Planes, Curve, Region of the Plane, Magnitude of Force

Typology: Exams

2012/2013

Uploaded on 02/14/2013

archan
archan 🇮🇳

3.8

(5)

92 documents

1 / 6

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Form A
Math 1224 Common Part of Final Exam December 18, 2001
INSTRUCTIONS: Please enter your NAME, ID NUMBER, FORM designation, and CRN on your op
scan sheet. The CRN should be written in the upper right-hand box labeled "Course." Do not include the
course number. In the box labeled "Form," write the appropriate test form letter shown above. Darken
the appropriate circles below your ID number and Form designation. Use a #2 pencil.
Mark your answers to the test questions in rows 1-16 of the op-scan sheet. You have 1 hour to complete
this part of the final exam. Your score on this part of the final exam will be the number of correct
answers. Turn in the op scan sheet with your answers and the question sheets, including this cover page,
at the end of this part of the final exam. Any additional parts of the exam will begin after all students
have completed this common part.
Exam Policies: You may not use a book, notes, formula sheet, or a calculator or computer. Giving or
receiving unauthorized aid is an Honor Code Violation.
Signature_________________________________________
Name (printed)_____________________________________
Student ID #_______________________________________
1. For two particular vectors
r
A
and
r
B
it is known that
rrrr
ABBA¥=¥
. What must be true about the two
vectors?
(1) At least one of the two vectors must be the zero vector.
(2)
rrrr
ABBA¥=¥
is true for any two vectors.
(3) One of the two vectors is a scalar multiple of the other vector.
(4) The two vectors must be perpendicular to each other.
2. Find the line of intersection of the two planes
23 3xyz+-=-
and
45 1xyz++=
. One point lying
on this line of intersection is
(, , )112-
.
(1)
86210xyz--=
(2)
xt
yt
zt
t
=+
=- -
=-
Ï
Ì
Ô
Ó
Ô-•< <•
14
13
2
(3)
xt
yt
zt
t
=+
=- -
=- +
Ï
Ì
Ô
Ó
Ô-•< <•
8
6
22
(4)
xt
yt
zt
t
=-
=- +
=-
Ï
Ì
Ô
Ó
Ô-•< <•
12
12
22
pf3
pf4
pf5

Partial preview of the text

Download Two Vectors - Vector Geometry - Exam and more Exams Computational Geometry in PDF only on Docsity!

Form A Math 1224 Common Part of Final Exam December 18, 2001

INSTRUCTIONS: Please enter your NAME, ID NUMBER, FORM designation, and CRN on your op scan sheet. The CRN should be written in the upper right-hand box labeled "Course." Do not include the course number. In the box labeled "Form," write the appropriate test form letter shown above. Darken the appropriate circles below your ID number and Form designation. Use a #2 pencil.

Mark your answers to the test questions in rows 1-16 of the op-scan sheet. You have 1 hour to complete this part of the final exam. Your score on this part of the final exam will be the number of correct answers. Turn in the op scan sheet with your answers and the question sheets, including this cover page, at the end of this part of the final exam. Any additional parts of the exam will begin after all students have completed this common part.

Exam Policies: You may not use a book, notes, formula sheet, or a calculator or computer. Giving or receiving unauthorized aid is an Honor Code Violation.

Signature_________________________________________

Name (printed)_____________________________________

Student ID #_______________________________________

  1. For two particular vectors

r A and

r B it is known that

r r r r A ¥ B = B ¥ A. What must be true about the two vectors?

(1) At least one of the two vectors must be the zero vector.

(2)

r r r r A ¥ B = B ¥ A is true for any two vectors.

(3) One of the two vectors is a scalar multiple of the other vector.

(4) The two vectors must be perpendicular to each other.

  1. Find the line of intersection of the two planes 2 x + 3 y - z = - 3 and 4 x + 5 y + z = 1. One point lying on this line of intersection is ( , 1 - 1 2 , ).

(1) 8 x - 6 y - 2 z = 10 (2)

x t y t z t

t

Ï

Ì

Ô

ÓÔ

x t y t z t

t

Ï

Ì

Ô

ÓÔ

x t y t z t

t

Ï

Ì

Ô

ÓÔ

  1. Identify the graph of the curve described by the parametric equations x t ( ) = e t^ , y t ( ) = e^2 t - 1 , 0 £ t < •.

(1)

x

1

2

y

(-1,0) (1,0) (0,-1)

-1 1 x

1

2

3

y

-1 x

1

2

y

(1,0) (0,-1)

-1 x

1

2

y

(1,0)

  1. The region of the plane for which 1 2 0 4 £ r £ £ £ cos( ) q and q p is:

x

y

1 2

x

y

1 2

x

y

1 2

x

y

1 2

  1. Which of the following diagrams correctly displays the three vectors

r r A , B and

r C if

r A and

r B are unit vectors and

r r r r r

C = A + 2 ( A B B ◊ )?

A^ ”

B^ ”

C^ ”

A^ ”

B^ ”

C^ ”

A^ ”

B^ ”

C^ ”^

A^ ”

B^ ”

C^ ”

  1. A projectile is launched horizontally with an initial speed of 96 ft/sec. Determine the slant range R to the point of impact. (Use g = 32 ft / sec .)^2

x

y g

30 o

R

(1) 144 3 ft (2) 384 ft (3) 432 ft (4) 480 ft

  1. Find the volume of the triangular prism shown. The base of the solid is a parallelogram shown in the accompanying figure.
  1. A car travels so that its normal component of acceleration at point A is twice as large as its normal component of acceleration at point B. Points A and B lie on portions of circular arcs having the radii shown. The speed of the car at point A is 40 ft/sec. What is the speed of the car at point B?

A

B

1000 ft

3000 ft

(1) 120 ft/sec (2) 80 ft/sec (3) 20 6 ft/sec (4) 80 3 ft/sec

  1. If r^

r r r x = ai + 2 j + ak and r^

r r r y = ai - 2 j - 3 k , for what value(s) of the constant a , if any, will the two vectors be perpendicular?

(1) a = - 1 and a = 4 (2) a = 0 and a = 3 (3) a = 1 and a = 3

(4) The two vectors are not perpendicular for any values of the constant a.

(0,0,0) (2,1,0)

(8,7,0)

(11,8,6)

(6,6,0)

(5,2,6)

x

y

z

x

y

(0,0,0)

(2,1,0)

(8,7,0) (6,6,0)

Base