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Math E21a – Fall 2009 – HW #1 problems
Due in class on Thurs, Sept 10
:
Section 9.1
:
8. Find the distance from (3, 7,–5) to each of the following.
(a) The
xy
plane
(b) The
yz
plane
(c) The
xz
plane
(d) The
x
axis
(e) The
y
axis
(f) The
z
axis
12. Find an equation of the sphere that passes through the origin and whose center is (1, 2, 3).
14. Show that the equation
222
4
4
4
8
16
1
x
yzxy
represents a sphere, and find its center and radius.
34. Consider the points
P
such that the distance from
P
to
A
(–1, 5, 3) is twice the distance from
P
to
B
(6, 2,–2). Show that the set of all such points is a sphere, and find its center and radius.
Section 9.2
:
20. Find a vector that has the same direction as
2,4,2
but has length 6.
24. Velocities have both magnitude and direction and thus are vectors. The magnitude of a velocity vector is
called
speed
. Suppose that a wind is blowing from
the direction N45
W at a speed of 50 km/h. (This means
that the direction from which the wind blows is 45
west of the northerly direction.) A pilot is steering a
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 Fall '09
 
 Math

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