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Byju's Answer
Standard XII
Mathematics
Applications of Cross Product
If a⃗=î+ĵ+k...
Question
If
→
a
=
^
i
+
^
j
+
^
k
,
→
b
=
^
i
+
^
j
−
^
k
,
→
c
=
^
i
−
^
j
+
^
k
and
→
d
=
^
i
−
^
j
−
^
k
, then
(
→
a
×
→
b
)
×
(
→
c
×
→
d
)
=
A
0
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B
3
^
i
−
5
^
j
+
7
^
k
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C
5
^
j
−
8
^
k
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D
−
8
^
k
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Solution
The correct option is
D
−
8
^
k
→
a
×
→
b
=
(
^
i
+
^
j
+
^
k
)
×
(
^
i
+
^
j
−
^
k
)
=
−
2
^
i
+
2
^
j
...(i)
→
c
×
→
d
=
(
^
i
−
^
j
+
^
k
)
×
(
^
i
−
^
j
−
^
k
)
=
2
^
i
+
2
^
j
...(ii)
Hence
(
−
2
^
i
+
2
^
j
)
×
(
2
^
i
+
2
^
j
)
=
−
4
^
k
−
4
^
k
=
−
8
^
k
Suggest Corrections
0
Similar questions
Q.
If
→
a
=
^
i
+
^
j
+
^
k
,
→
b
=
^
i
+
^
j
−
^
k
,
→
c
=
^
i
−
^
j
+
^
k
,
→
d
=
^
i
−
^
j
−
^
k
then
|
(
→
a
×
→
b
)
.
(
→
c
×
→
d
)
|
=
Q.
If
→
a
=
2
^
i
+
^
j
−
3
^
k
,
→
b
=
^
i
−
2
^
j
+
^
k
,
→
c
=
−
^
i
+
^
j
−
4
^
k
and
→
d
=
^
i
+
^
j
+
^
k
, then
|
(
→
a
×
→
b
)
×
(
→
c
×
→
d
)
|
Q.
If
→
a
=
^
i
+
^
j
+
^
k
,
→
b
=
^
i
−
^
j
+
^
k
,
→
c
=
^
i
+
^
j
−
^
k
and
→
a
=
^
i
−
^
j
−
^
k
, then
(
→
a
×
→
b
)
×
(
→
c
×
→
d
)
is a vector orthogonal to both
Q.
Vectors
→
a
=
3
^
i
+
^
j
+
^
k
,
→
b
=
^
i
−
^
j
+
2
^
k
a
n
d
→
c
=
2
^
i
−
^
j
−
^
k
. Find vector
→
d
if
¯
d
is perpendicular to
→
c
and
→
d
.
→
a
=
10
,
→
b
=
1
Q.
If
→
a
=
2
^
i
+
3
^
j
+
^
k
,
→
b
=
^
i
−
^
j
+
^
k
,
→
c
=
^
i
+
^
j
+
^
k
and let
→
d
be such that
→
a
×
→
b
=
→
d
×
→
b
,
→
d
⋅
→
c
=
8
, then the value of
→
d
.
→
b
is
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