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)
Exercise 4.3 (page 158)
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.
Exercise 4.5 (page 165)
Technical Computing Exercises 4.7
REVIEW EXERCISES 4
Ans:
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.
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
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.
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.
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)
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
Ans:
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