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Byju's Answer
Standard XII
Physics
Vector Addition
If a, → b, → ...
Question
If
a
,
→
b
,
→
c
→
are non-coplanar vectors, then find the value of
a
→
·
b
→
×
c
→
c
→
×
a
→
·
b
→
+
b
→
·
a
→
×
c
→
c
→
·
a
→
×
b
→
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Solution
We
have
a
→
.
b
→
×
c
→
c
→
×
a
→
.
b
→
+
b
→
.
a
→
×
c
→
c
→
.
a
→
×
b
→
=
a
→
b
→
c
→
c
→
a
→
b
→
+
b
→
a
→
c
→
c
→
a
→
b
→
By
definition
of
scalar
triple
product
=
a
→
b
→
c
→
a
→
b
→
c
→
+
-
a
→
b
→
c
→
a
→
b
→
c
→
Change
of
cyclic
order
of
vectors
changes
the
sign
of
the
scalar
triple
product
=
1
-
1
=
0
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1
Similar questions
Q.
If
a
→
,
b
→
,
c
→
are non-coplanar vectors, then
b
→
×
c
→
,
a
→
+
b
→
+
c
→
a
→
b
→
c
→
= _______________.
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
)
Q.
If
a
,
→
b
,
→
c
→
are three non-coplanar vectors, then
a
→
+
b
→
+
c
→
.
a
→
+
b
→
×
a
→
+
c
→
equals
(a) 0
(b)
a
→
b
→
c
→
(c)
2
a
→
b
→
c
→
(d)
-
a
→
b
→
c
→
Q.
If
a
,
b
,
c
are non-coplanar vectors then find the value of
(
a
+
2
b
−
c
)
.
(
a
−
b
)
×
(
a
−
b
−
c
)
[
a
b
c
]
Q.
Assertion :If
a
,
b
,
c
are three non-coplanar, non-zero vectors, then
(
a
.
a
)
b
×
c
+
(
a
.
b
)
c
×
a
+
(
a
.
c
)
a
×
b
=
[
b
c
a
]
a
Reason: If the vectors
a
,
b
,
c
are non-coplanar, then so are
b
×
c
,
c
×
a
,
a
×
b
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