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Byju's Answer
Standard XII
Mathematics
Applications of Cross Product
Let the pairs...
Question
Let the pairs
→
a
,
→
b
and
→
c
,
→
d
each determine a plane, then the planes are parallel if
A
(
→
a
×
→
c
)
×
(
→
b
×
→
d
)
=
→
0
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B
(
→
a
×
→
c
)
⋅
(
→
b
×
→
d
)
=
→
0
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C
(
→
a
×
→
b
)
×
(
→
c
×
→
d
)
=
→
0
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D
(
→
a
×
→
b
)
⋅
(
→
c
×
→
d
)
=
→
0
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Solution
The correct option is
C
(
→
a
×
→
b
)
×
(
→
c
×
→
d
)
=
→
0
→
a
×
→
b
is a vector perpendicular to the plane contining
→
a
and
→
b
.
Similarly,
→
c
×
→
d
is a vector perpendicular to the plane containing
→
c
and
→
d
.
Thus, the two planes will be parallel if their normals,
i.e.,
→
a
×
→
b
and
→
c
×
→
d
, are parallel.
Thus,
(
→
a
×
→
b
)
×
(
→
c
×
→
d
)
=
→
0
Hence, option
C
.
Suggest Corrections
0
Similar questions
Q.
Let the Vectors
→
a
,
→
b
,
→
c
,
→
d
be such that
(
→
a
×
→
b
)
×
(
→
c
×
→
d
)
=
→
0
. Let
p
1
,
p
2
be planes determinated by the pair of vectors
→
a
,
→
b
and
→
c
,
→
d
respectively, then the angle between
p
1
, and
p
2
as
Q.
If
→
A
+
→
B
+
→
C
+
→
D
=
→
0
then
∣
∣
→
A
+
→
C
∣
∣
is equal to :
Q.
Let the vectros
→
a
,
→
b
,
→
c
and
→
d
be such that
(
→
a
×
→
b
)
×
(
→
c
×
→
d
)
=
→
0
.
Let
P
1
and
P
2
be planes determined by pairs of vectros
→
a
,
→
b
and
→
c
,
→
d
,
respectively. Then the angle between
P
1
and
P
2
is
Q.
If
→
a
,
→
b
,
→
c
,
→
d
are non-coplanar vectors then the vector
(
→
a
×
→
b
)
×
(
→
c
×
→
d
)
+
(
→
a
×
→
c
)
×
(
→
d
×
→
b
)
+
(
→
a
×
→
d
)
×
(
→
b
×
→
c
)
is parallel to:
Q.
If
→
a
×
→
b
=
→
c
×
→
d
and
→
a
×
→
c
=
→
b
×
→
d
, then
→
a
−
→
d
,
→
b
−
→
c
are
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