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Byju's Answer
Standard XII
Physics
Work Done as Dot Product
If |a| = |b|=...
Question
If
|
→
a
|
=
|
→
b
|
=
|
→
c
|
=
2
and
→
a
⋅
→
b
=
→
b
⋅
→
c
=
→
c
⋅
→
a
=
2
,
then
[
→
a
→
b
→
c
]
cos
45
∘
is equal to
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Solution
[
→
a
→
b
→
c
]
2
=
∣
∣ ∣ ∣ ∣
∣
→
a
.
→
a
→
a
.
→
b
→
a
.
→
c
→
b
.
→
a
→
b
.
→
b
→
b
.
→
c
→
c
.
→
a
→
c
.
→
b
→
c
.
→
c
∣
∣ ∣ ∣ ∣
∣
=
∣
∣ ∣
∣
4
2
2
2
4
2
2
2
4
∣
∣ ∣
∣
=
32
[
→
a
→
b
→
c
]
=
4
√
2
⇒
[
→
a
→
b
→
c
]
cos
45
∘
=
4
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1
Similar questions
Q.
If
|
a
|
=
2
,
|
b
|
=
3
,
|
c
|
=
4
and
a
+
b
+
c
=
0
then the value of
b
⋅
c
+
c
⋅
a
+
a
⋅
b
is equal to
Q.
If a,b,c,d are four vectors, then prove that
(a×b).(c×d)+(b×c).(a×d)+(c×a).(b×d)=0
Q.
The value of
(
a
×
b
)
⋅
(
c
×
d
)
+
(
b
×
c
)
⋅
(
a
×
d
)
+
(
c
×
a
)
⋅
(
b
×
d
)
is
Q.
Let
→
a
,
→
b
and
→
c
be three unit vectors such that
→
a
+
→
b
+
→
c
=
→
0
. If
λ
=
→
a
⋅
→
b
+
→
b
⋅
→
c
+
→
c
⋅
→
a
and
→
d
=
→
a
×
→
b
+
→
b
×
→
c
+
→
c
×
→
a
, then the ordered pair
(
λ
,
→
d
)
is equal to:
Q.
If
A
,
B
,
C
are three non-coplanar vectors, then find the value of
A
⋅
(
B
×
C
)
(
C
×
A
)
⋅
B
+
B
⋅
(
A
×
C
)
C
⋅
(
A
×
B
)
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