18. The matrix corresponding to a 6-fold rotation along z-axis using orthogonal
system is:
(a)
1=2 À
ffiffi ffi
3
p =2 0
ffiffi ffi
3
p =2
1=2
0
0
0
1
0
@
1
A
(b)
À1=2
ffiffi ffi
3
p =2 0
À
ffiffi ffi
3
p =2 À1=2 0
0
0
1
0
@
1
A
(c)
1=2
ffiffi ffi
3
p =2 0
À
ffiffi ffi
3
p =2 1=2 0
0
0
1
0
@
1
A
(d)
À1=2 À
ffiffi ffi
3
p =2 0
ffiffi ffi
3
p =2 À1=2 0
0
0
1
0
@
1
A
19. The matrix corresponding to a 6-fold rotation along z-axis using orthogonal
system is:
(a)
1=2 À
ffiffi ffi
3
p =2 0
ffiffi ffi
3
p =2
1=2
0
0
0
1
0
@
1
A
(b)
À1=2
ffiffi ffi
3
p =2 0
À
ffiffi ffi
3
p =2 À1=2 0
0
0
1
0
@
1
A
(c)
1=2
ffiffi ffi
3
p =2 0
À
ffiffi ffi
3
p =2 1=2 0
0
0
1
0
@
1
A
(d)
À1=2 À
ffiffi ffi
3
p =2 0
ffiffi ffi
3
p =2 À1=2 0
0
0
1
0
@
1
A
20. The matrix corresponding to a 3-fold rotation along z-axis using crystallographic system is:
(a)
À1 1 0
À1 0 0
0 0 À1
0
@
1
A
(b)
1 À1 0
1 0 0
0 0 1
0
@
1
A
(c)
0 1 0
À1 1 0
0 0 À1
0
@
1
A
(d)
0 À1 0
1 À1 0
0 0 1
0
@
1
A
6.3 Group (Point) Representation of Symmetry Operations
255