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beFore answering.
001
10.0 points
A rectangular box is constructed in 3-space
with one corner at the origin and other ver-
tices at
(4
,
0
,
0)
,
(0
,
3
,
0)
,
(0
,
0
,
1)
.
±ind the length oF the diagonal oF the box.
1.
length = 19
2.
length =
√
26
correct
3.
length =
√
34
4.
length = 34
5.
length = 26
6.
length =
√
19
Explanation:
We have to fnd the length oF
BD
in the
fgure
O
D
A
B
G
F
C
E
given that
OA
= 4
, OC
= 3
, OD
= 1
.
Now by Pythagoras’ theorem,
length
OB
= length
AC
= 5
.
But then, again by Pythagoras,
length
BD
=
√
26
.
Consequently,
length =
√
26
.
keywords: length diagonal, rectangular solid,
Pythagoras’ theorem
002
10.0 points
Determine the distance oF the point
Q
(
−
4
,
2
,
1)
From the
z
-axis.
1.
distance = 1
2.
distance =
√
5
3.
distance = 2
4.
distance =
√
21
5.
distance = 4
6.
distance =
√
17
7.
distance = 2
√
5
correct
Explanation:
Since the distance oF a point
P
(
x, y, z
)
From the
z
-,
x
-, and
y
-axes is given respec-
tively by
r
x
2
+
y
2
,
r
y
2
+
z
2
,
r
z
2
+
x
2
,
the point
Q
(
−
4
,
2
,
1) has
distance = 2
√
5
From the
z
-axis.
keywords:
coordinate plane,
projection,
point, distance, 3-space
003
10.0 points
Which oF the Following statements are true: