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Byju's Answer
Standard XII
Mathematics
Addition of Vectors
For any 3 vec...
Question
For any 3 vectors
→
a
→
b
and
→
c
prove that
[
→
a
+
→
b
→
b
+
→
c
→
c
+
→
a
]
=
2
[
→
a
→
b
→
c
]
Open in App
Solution
S
i
n
c
e
,
(
→
a
+
→
b
)
×
(
→
b
+
→
c
)
=
→
a
×
→
b
+
→
a
×
→
c
N
o
w
,
l
e
t
E
=
[
→
a
+
→
b
→
b
+
→
c
→
c
+
→
a
]
E
=
[
→
a
×
→
b
+
→
a
×
→
c
+
→
b
×
→
c
]
⋅
(
→
c
+
→
a
)
E
=
[
→
a
→
b
→
c
]
+
[
→
a
→
b
→
c
]
E
=
2
[
→
a
→
b
→
c
]
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0
Similar questions
Q.
For non-zero vectors
→
a
,
→
b
,
→
c
;
∣
∣
∣
(
→
a
×
→
b
)
⋅
→
c
∣
∣
∣
=
∣
∣
→
a
∣
∣
∣
∣
∣
→
b
∣
∣
∣
∣
∣
→
c
∣
∣
holds if and only if
Q.
If
[
→
a
+
→
b
→
b
+
→
c
→
c
+
→
a
]
=
λ
1
[
→
a
→
b
→
c
]
and
[
→
a
×
→
b
→
b
×
→
c
→
c
×
→
a
]
=
[
→
a
→
b
→
c
]
λ
2
then
λ
1
+
λ
2
3
is (where
→
a
,
→
b
,
→
c
are non zero and non coplanar vectors)
Q.
L
e
t
→
a
=
^
i
−
^
j
,
→
b
=
^
j
−
^
k
,
→
c
=
^
k
−
^
i
.
If
→
d
is a unit vector such that
→
a
⋅
→
d
=
0
=
[
→
b
→
c
→
d
]
,
then
→
d
Q.
If
(
→
A
+
→
B
)
.
(
→
A
−
→
B
)
=
0
t
h
e
n
→
A
:
→
B
is equal to
Q.
The value of
[
→
a
−
→
b
→
b
−
→
c
→
c
−
→
a
]
where
|
→
a
|
=
1
,
|
→
b
|
=
5
,
|
→
c
|
=
3
, is
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