082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

158 Chapter 4 Coordinate systems
x
2
1
z
4
3
2
1
O
3
1
4
P (2, 3, 4)
2
2
3 y
Figure4.6
Cartesian coordinate systemin three
dimensions.
A
x
–1
1
z
2
1
C
1
B
2 y
Figure4.7
ThepointsA, Band Care
plotted in threedimensions.
AandBinFigure4.7lieintheplanez = 2.Allpointsinthisplanehaveazcoordinate
of 2.
EXERCISES4.3
1 Plotthe pointsA(2,0, −1),B(1, −1,1)and
C(−1,1,2).
2 Statethe equationofthe planepassingthrough
(4,7, −1),(3,0,−1) and(1,2, −1).
3 Statethe equationofthe planepassingthrough
(3,1,7),(−1,1,0)and(6,1, −3).
Solutions
1 FigureS.7 illustratesthe pointsA, B andC.
3 y=1
2 z=−1
B (1, –1, 1)
x
2
FigureS.7
–1
1
z
2
1
A (2, 0, –1)
–1
–1
1
C (–1, 1, 2)
2 y
y
O
u
r
x
P (x, y)
y
A
Figure4.8
Phas polar coordinatesrand θ.
x