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Byju's Answer
Standard XII
Mathematics
Definition of Vector
For non-zero ...
Question
For non-zero vectors
→
a
,
→
b
,
→
c
,
|
→
a
×
→
b
×
→
c
|
=
|
→
a
|
|
→
b
|
|
→
c
|
holds if and only if:
A
→
a
.
→
b
=
0
,
→
b
,
→
c
=
0
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B
→
c
.
→
a
=
0
,
→
a
,
→
b
=
0
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C
→
a
.
→
c
=
0
,
→
b
,
→
c
=
0
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D
→
a
.
→
b
=
→
b
.
→
c
=
→
a
.
→
a
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Solution
The correct option is
D
→
a
.
→
b
=
→
b
.
→
c
=
→
a
.
→
a
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0
Similar questions
Q.
Three vectors
→
a
,
→
b
,
→
c
. Satisfy the condition
→
a
+
→
b
+
→
c
=
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. Evaluate
μ
=
→
a
.
→
b
+
→
b
.
→
c
+
→
c
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→
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|
→
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|
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;
∣
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→
b
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=
4
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|
→
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.
Q.
If
→
a
,
→
b
,
→
c
are vectors such that
→
a
.
→
b
=
→
a
.
→
c
,
→
a
×
→
b
=
→
a
×
→
c
,
→
a
≠
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, Then show that
→
b
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.
Q.
If
→
a
,
→
b
,
→
c
are unit vectors such that
→
a
+
→
b
+
→
c
=
0
, then the
→
a
.
→
b
+
→
b
.
→
c
+
→
c
.
→
a
=
Q.
If
(
→
a
×
→
b
)
×
→
c
=
→
a
×
(
→
b
×
→
c
)
where
→
a
,
→
b
and
→
c
are any three vectors such that
→
a
.
→
b
≠
0
,
→
b
.
→
c
≠
0
then
→
a
and
→
c
are
Q.
Three vectors
|
→
a
|
,
∣
∣
→
b
∣
∣
and
|
→
c
|
satisfy the condition
→
a
+
→
b
+
→
c
=
0
.
Evaluate the quantity
λ
=
→
a
.
→
b
+
→
b
.
→
c
+
→
c
.
→
a
, if
|
→
a
|
=
1
,
∣
∣
→
b
∣
∣
=
4
a
n
d
|
→
c
|
=
2
.
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