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Byju's Answer
Standard XII
Physics
Displacement in 2D Motion
If a⃗,b⃗ an...
Question
If
→
a
,
→
b
and
→
c
are non coplanar unit vectors such that
→
a
×
→
b
×
→
c
=
→
b
+
→
c
√
2
then the angle between
A
→
a
&
→
b
is
3
π
4
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B
→
a
&
→
b
is
π
4
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C
→
a
&
→
c
is
3
π
4
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D
→
a
&
→
c
is
π
4
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Solution
The correct options are
A
→
a
&
→
b
is
3
π
4
D
→
a
&
→
c
is
π
4
→
a
×
(
→
b
×
→
c
)
=
→
b
+
→
c
√
2
⇒
(
→
a
.
→
c
)
→
b
−
(
→
a
.
→
b
)
→
c
=
→
b
√
2
+
→
c
√
2
⇒
(
→
a
.
→
c
−
1
√
2
)
→
b
−
(
→
a
.
→
b
+
1
√
2
)
→
c
=
0
∴
→
a
.
→
b
=
−
1
√
2
and
→
a
.
→
c
=
1
√
2
Hence
Angle between
→
a
and
→
b
is
cos
−
1
(
−
1
√
2
)
=
3
π
4
And angle between
→
a
and
→
c
is
cos
−
1
(
1
√
2
)
=
π
4
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Similar questions
Q.
If
→
a
,
→
b
,
→
c
are unit vectors such that
→
a
+
→
b
+
→
c
=
→
0
and
(
→
a
,
→
b
)
=
π
3
, then
∣
∣
→
a
×
→
b
∣
∣
+
∣
∣
→
b
×
→
c
∣
∣
+
|
→
c
×
→
a
|
=
Q.
If
→
a
,
→
b
,
→
c
are non-coplanar unit vectors such that
→
a
×
(
→
b
×
→
c
)
=
(
→
b
+
→
c
)
√
2
,
then the angle between
→
a
and
→
b
is
Q.
If
→
a
,
→
b
,
→
c
are non coplanar vectors such that
→
b
×
→
c
=
→
a
,
→
c
×
→
a
=
→
b
and
→
a
×
→
b
=
→
c
, then
Q.
If
→
a
,
→
b
,
→
c
are unit vectors and the angles between
→
a
,
→
b
and
→
b
,
→
c
and
→
c
,
→
a
are
π
6
,
π
3
and
π
4
respectively, then
|
→
a
+
→
b
+
→
c
|
Q.
If
→
a
,
→
b
,
→
c
are non-coplanar non-zero vectors such that
→
b
×
→
c
=
→
a
,
→
a
×
→
b
=
→
c
,
→
c
×
→
a
=
→
b
, then
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