C
HAPTER
1
1. The vectors
ˆ
ˆ
ˆ
+
+
x
y
z
and
ˆ
ˆ
ˆ
−
−
+
x
y
z
are in the directions of two body diagonals of a
cube. If
θ
is the angle between them, their scalar product gives cos
θ
= –1/3, whence
.
1
cos
1/3
90
19 28'
109 28'
−
θ =
=
°+
°
=
°
2. The plane (100) is normal to the x axis. It intercepts the
a'
axis at
and the
c'
axis
at
; therefore the indices referred to the primitive axes are (101). Similarly, the plane
(001) will have indices (011) when referred to primitive axes.
2a'
2c'
3. The central dot of the four is at distance
cos60
a
ctn 60
cos30
3
a
a
°
=
° =
°
from each of the other three dots, as projected onto the basal plane. If
the (unprojected) dots are at the center of spheres in contact, then
2
2
2
a
c
a
,
2
3
⎛
⎞
⎛
⎞
=
+
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
or
2
2
2
1
c
8
a
c ;
1.633.
3
4
a
3
=
=
1-1

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