Skip to main content

Exercise Chapter 4: Coordinate systems Book Engineering Mathematics A Foundation for Electronic, Electrical, Communications and Systems Engineers.

Exercise 4.2  (page 157)
1. Plot the following points: A(2,−2), B(−2, 1),
C(−1, 0), D(0,−2).
2. State the coordinates of the points U, V and W .
3. A point P lies on the x axis. State the y coordinate of P.

4. A point Q lies on the y axis. State the x coordinate of Q.

Ans:

  1. We have points: A(2, -2) , B(-2, 1) , C(-1, 0) , D(0, -2)


 2. State the coordinates of the points :

     U(−2,−2), V(4, 1), W(3,−1)

 3. A point P lies on the x axis. State the y coordinate of P.

      P(0, 0)
 4. A point Q lies on the y axis. State the x coordinate of Q.

      Q(0, 0)
Exercise 4.3  (page 158)

1. Plot the points A(2, 0,−1), B(1,−1, 1) and
C(−1, 1, 2).
2. State the equation of the plane passing through
(4, 7,−1), (3, 0,−1) and (1, 2,−1).

3. State the equation of the plane passing through

(3, 1, 7), (−1, 1, 0) and (6, 1,−3).

Ans:

 1.We have 3 points:
        A(2, 0,−1) , B(1,−1, 1) , C(−1, 1, 2)

 2.State the equation of the plane passing through
(4, 7,−1), (3, 0,−1) and (1, 2,−1).


 In the graph lie in the plane z = -1. All points in this plane have a z coordinate of -1.

 3. State the equation of the plane passing through
(3, 1, 7), (−1, 1, 0) and (6, 1,−3).


In the graph lie in the plane y = 1. All points in this plane have a y coordinate of 1.

 Exercise 4.4  (page 163)












Ans:

 1 .Given the polar coordinates, calculate the Cartesian coordinates of each point.



2. Given the Cartesian coordinates, calculate the polar
coordinates of each point.



Exercise 4.5  (page 165)








Ans:
1.



2. 



Exercise 4.6  (page 170)


Ans:

1.Express the following Cartesian coordinates as cylindrical polar coordinates.

2. Express the following cylindrical polar coordinates as
Cartesian coordinates.

3. Describe the surface defined by
   a) z = 0
     z in the space
     x and y in the plane

    b) z = -1
      a plane parallel to the x--y plane and 1 unit below it

   c) r = 2, z = 1
      a circle, radius 2, parallel to the x--y plane and with center at 
(0, 0, 1)




Exercise 4.7  (page 173)

Ans:



Technical Computing Exercises 4.7




REVIEW EXERCISES 4

Ans:



















































Labels:

Comments

Post a Comment

Popular posts from this blog

The laws of set algebra & Laws derivable >> in the table 5.1 & 5.2 :

Ans :       Commutative laws                             Ans:          Associative laws Ans:         Distributive laws       Ans:            Identity laws Ans:         Complement laws Ans:          Absorption laws Ans:         Minimization laws Ans:         De Morgan’s laws
Post a Comment
Read more

Matrix algebra

                 Matrices provide a means of storing large quantities of information in such a way that each piece can be easily identified and manipulated. They permit the solution of large systems of linear equations to be carried out in a logical and formal way so that computer implementation follows naturally. Applications of matrices extend over many areas of engineering including electrical network analysis and robotics. 1-BASIC DEFINITIONS                  Matrix is a rectangular pattern or array of numbers.      For example:                    are all matrices. Note that we usually use a capital letter to denote a matrix, and enclose the array of numbers in brackets. To describe the size of a matrix we quote its number of rows and columns in that order so, for example, an r × s matrix has r rows and s colu...
2 comments
Read more

Discrete mathematics

            It's about Discrete mathematics in this book  #Anthony Croft, Engineering Mathematices, 5e (2017)  So i will choose exercise 5.2 #7 #8 #9  to slow everyone: 7 . The sets A, B and C are given by A = {1, 3, 5, 7, 9}, B = {0, 2, 4, 6} and C = {1, 5, 9} and the universal set, E = {0,1, 2, . . . ,9}. (a) Represent the sets on a Venn diagram. (b) State A ∪ B. (c) State B ∩ C. (d) State E ∩ C. (e) State not A. (f) State not B ∩not C. (g) State not (B ∪C). Ans :  a ) Represent the sets on a Venn diagram : The set containing all the numbers of interest is called the universal set, E. E is represented by the rectangular region. Sets A , B and C are represented  by the interiors of the circles and it is evident that 1 ,   3,  5,  7 and 9 are members of A while 0, 2,  4,  and 6 are members of B that 1,  5  and  9 are members of C....
Post a Comment
Read more