2
You visited us
2
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Physics
Work Done as Dot Product
Prove that fo...
Question
Prove that for any three vectors
→
a
,
→
b
and
→
c
,
[
(
→
a
+
→
b
)
(
→
b
+
→
c
)
(
→
c
+
→
a
)
]
=
2
[
→
a
→
b
→
c
]
.
Open in App
Solution
LHS:
[
(
→
a
+
→
b
)
(
→
b
+
→
c
)
(
→
c
+
→
a
)
]
=
(
→
a
+
→
b
)
.
[
→
b
+
→
c
×
→
c
+
→
a
]
=
(
→
a
+
→
b
)
.
[
→
b
×
→
c
+
→
b
×
→
a
+
→
c
×
→
c
+
→
c
×
→
a
]
=
→
a
.
(
→
b
×
→
c
)
+
→
b
.
(
→
c
×
→
a
)
=
[
→
a
→
b
→
c
]
+
[
→
b
→
c
→
a
]
⇒
2
[
→
a
→
b
→
c
]
=
RHS
Hence proved.
Suggest Corrections
0
Similar questions
Q.
If
→
a
,
→
b
,
→
c
be any three non - coplanar vectors, then calculate the value of
[
→
a
+
→
b
→
b
+
→
c
→
c
+
→
a
]
is
Q.
For any three vectors
→
a
,
→
b
a
n
d
→
c
,
[
→
a
+
→
b
→
b
+
→
c
→
c
+
→
a
]
=
.
Q.
If
→
a
,
→
b
,
→
c
are three vectors such that
→
a
,
→
b
,
→
c
, then prove that
→
a
×
→
b
=
→
b
×
→
c
=
→
c
×
→
a
, and hence show that
[
→
a
→
b
→
c
]
=
0.
Q.
If
→
a
,
→
b
,
→
c
are three vectors such that
→
a
+
→
b
+
→
c
=
→
0
,
then prove that
→
a
×
→
b
=
→
b
×
→
c
=
→
c
×
→
a
,
and hence show that
[
→
a
→
b
→
c
]
=
0.
Q.
[
(
→
a
×
→
b
)
×
(
→
b
×
→
c
)
(
→
b
×
→
c
)
×
(
→
c
×
→
a
)
(
→
c
×
→
a
)
×
(
→
a
×
→
b
)
]
[
→
a
×
→
b
→
b
×
→
c
→
c
×
→
a
]
is equal to
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
The Work Done as a Dot-Product
PHYSICS
Watch in App
Explore more
CBSE Board
Work Done as Dot Product
Standard XII Physics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app