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Byju's Answer
Standard XII
Mathematics
Definition of Vector
If 2î and ...
Question
If
2
^
i
and
^
j
+
√
3
^
j
are the vectors representing sides
A
B
and
B
C
respectively of a regular hexagon
A
B
C
D
E
F
. Express vectors
¯
¯¯¯¯¯¯¯
¯
C
D
,
¯
¯¯¯¯¯¯¯
¯
D
E
,
¯
¯¯¯¯¯¯
¯
F
A
,
¯
¯¯¯¯¯¯
¯
A
C
,
¯
¯¯¯¯¯¯¯
¯
A
D
,
¯
¯¯¯¯¯¯
¯
A
E
,
¯
¯¯¯¯¯¯
¯
C
E
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Solution
The required vector of given sides are-
−
−
−
→
A
B
=
+
−
−
→
D
E
=
−
2
ˆ
i
−
−
→
A
C
=
−
−
→
A
B
+
−
−
→
B
C
=
2
ˆ
i
+
(
1
+
√
3
)
ˆ
j
−
−
→
B
C
+
−
−
→
D
E
=
−
−
→
C
D
=
−
2
ˆ
i
+
(
1
+
√
3
)
ˆ
j
−
−
→
F
A
=
−
−
→
E
F
+
−
−
→
A
B
=
−
−
−
→
B
C
+
−
−
→
A
B
=
2
ˆ
i
−
(
1
+
√
3
)
ˆ
j
−
−
→
A
D
=
−
−
→
A
C
+
−
−
→
C
D
=
2
ˆ
i
+
(
1
+
√
3
)
ˆ
j
+
(
−
2
ˆ
i
)
+
(
1
+
√
3
)
ˆ
j
=
2
(
1
+
√
3
)
ˆ
j
−
−
→
A
E
=
−
−
→
A
D
+
−
−
→
D
E
=
−
2
ˆ
i
+
(
1
+
√
3
)
ˆ
j
−
−
→
C
E
=
−
−
→
C
D
+
−
−
→
D
E
=
−
2
ˆ
i
+
(
1
+
√
3
)
ˆ
j
−
2
ˆ
i
+
(
1
+
√
3
)
ˆ
J
Which is the required given answer.
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Similar questions
Q.
If a,b represent
−
−
→
A
B
,
−
−
→
B
C
respectively of a regular hexagon ABCDEF then
−
−
→
C
D
,
−
−
→
D
E
,
−
−
→
E
F
,
−
−
→
F
A
are
Q.
A
B
C
D
E
F
is a regular hexagon. If
^
A
B
=
^
a
and
^
B
C
=
^
b
then the other sides are represented by the vectors
Q.
If
a
and
b
represent the sides
−
−
→
A
B
and
−
−
→
B
C
OF regular hexagon ABCDEF than
−
−
→
F
A
Q.
ABCDEF is a regular hexagon . Let
→
A
B
=
a
and
→
B
C
=
b
. Express the vectors
→
A
C
in terms if a and b.
Q.
In a
△
A
B
C
,
D
and
E
are points on the sides
A
B
and
A
C
respectively such that
D
E
∥
B
C
. If
A
D
=
2.4
c
m
,
A
E
=
3.2
c
m
,
D
E
∥
B
C
. If
A
D
=
2.4
c
m
,
A
E
=
3.2
c
m
,
D
E
=
2
c
m
and
B
C
=
5
c
m
, find
B
D
and
C
E
.
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