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STCTIO!I
I2.I IlREE.t)IMENSIONAL
(OORDINATE
SYSITMS
.
797
l2.l Exercises
l.
Suppose
you start at the origin, move along the xaxis a
distance
of 4 units in the positive direction, and then move
downward
a distance of 3 units. What are the coordinates
of
your position?
l.
Sketch
the points
(0,5,2),
(4,0,
I),(2,4,6),
and
(1,
1,2)
on a single set of coordinate axes.
3.
Which of the points P(6,2,3),
Qes,
L,4),
and R(0, 3, 8)
is
closest
to the xzplane? Which point lies in the yzplane?
4. What are the projections of the point (2, 3, 5) on the xy, yz,
and xzplanes? Draw a rectangular box with the origin and
(2,3,5) as opposite
vertices and with its faces parallel
to the
coordinate planes. Label all vertices of the box. Find the length
of the diagonal of the box.
5. Describe and sketch
the surface
in R3 represented
by the equa
tionxiy:2.
6.
(a) What does
the equation
r
:
4 represent
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 Spring '08
 WORMER
 Math

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