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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:



















































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