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Byju's Answer
Standard IX
Mathematics
Properties of Parallelogram
ABCDEF are th...
Question
A
B
C
D
E
F
are the vertices of a regular hexagon.
→
A
B
=
→
a
,
→
B
C
=
→
b
, then the vectors of
¯
¯¯¯¯¯¯
¯
A
E
and
¯
¯¯¯¯¯¯
¯
E
F
are
A
→
a
−
→
b
,
→
a
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B
→
b
−
→
a
,
→
a
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C
2
→
b
−
→
a
,
−
→
b
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D
→
a
−
→
b
,
→
b
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Solution
The correct option is
B
2
→
b
−
→
a
,
−
→
b
−
−
→
A
E
=
−
−
→
A
B
+
−
−
→
B
C
+
−
−
→
C
D
+
−
−
→
D
E
=
→
a
+
→
b
+
→
b
−
→
a
−
→
a
=
2
→
b
−
→
a
−
−
→
E
F
|
|
−
−
→
B
C
−
−
→
E
F
=
−
−
−
→
B
C
−
−
→
E
F
=
−
→
b
−
−
→
E
F
=
−
→
K
b
(
a
s
−
−
→
A
D
|
|
−
−
→
B
C
)
|
−
−
→
A
D
|
=
2
→
b
(
a
s
|
→
a
|
=
|
→
b
|
r
e
g
u
l
o
r
h
e
x
o
g
o
n
)
−
−
→
A
D
=
−
−
→
A
B
+
−
−
→
B
C
+
−
−
→
C
D
−
−
→
C
D
=
→
b
−
→
a
Suggest Corrections
0
Similar questions
Q.
ABCD is parallelogram. If
→
A
B
=
→
a
,
→
B
C
=
→
b
then show that
→
A
B
=
→
a
,
+
→
b
and
→
B
D
=
→
b
,
−
→
a
?
Q.
Let
→
A
=
→
b
×
→
c
,
→
B
=
→
c
×
→
a
,
→
C
=
→
a
×
→
b
, then the vectors
→
A
×
(
→
B
×
→
C
)
,
→
B
×
(
→
C
×
→
A
)
, and
→
C
×
(
→
A
×
→
B
)
are
Q.
I : If
|
→
a
+
→
b
|
=
|
→
a
−
→
b
|
, then
(
→
a
,
→
b
)
=
π
2
.
II : If
→
a
,
→
b
,
→
a
+
→
b
are unit vectors, then
(
→
a
,
→
b
)
=
2
π
3
.
Q.
Show that vectors
|
→
b
|
→
a
+
|
→
a
|
→
b
and
|
→
b
|
→
a
−
|
→
a
|
→
b
are orthogonal.
Q.
If
→
a
and
→
b
are unequal vectors such that
(
→
a
−
→
b
)
×
[
(
→
b
+
→
a
)
×
(
2
→
a
+
→
b
)
]
=
→
a
+
→
b
, then the angle
θ
between
→
a
and
→
b
is
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