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Byju's Answer
Standard XII
Mathematics
Applications of Cross Product
Let a⃗=i⃗+j...
Question
Let
→
a
=
→
i
+
→
j
+
→
k
,
→
c
=
→
j
−
→
k
. If
→
b
is a vector satisfying
→
a
×
→
b
=
→
c
and
→
a
.
→
b
=
3
, then
→
b
is
A
1
3
(
5
→
i
+
2
→
j
+
2
→
k
)
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B
1
3
(
5
→
i
−
2
→
j
−
2
→
k
)
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C
(
3
→
i
−
2
→
j
−
→
k
)
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D
1
3
(
3
→
i
−
→
j
−
→
k
)
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Solution
The correct option is
B
1
3
(
5
→
i
+
2
→
j
+
2
→
k
)
Now,
→
a
×
→
b
=
∣
∣ ∣ ∣
∣
ˆ
i
ˆ
j
ˆ
k
1
1
1
b
1
b
2
b
3
∣
∣ ∣ ∣
∣
=
ˆ
i
(
b
3
−
b
2
)
−
ˆ
j
(
b
3
−
b
1
)
+
ˆ
k
(
b
2
−
b
1
)
=
ˆ
j
−
ˆ
k
⇒
b
3
−
b
2
=
−
1............
(
1
)
⇒
b
3
−
b
1
=
−
1.............
(
2
)
S
u
b
s
t
r
a
c
t
i
n
g
(
1
)
−
(
2
)
w
e
g
e
t
,
b
3
−
b
2
=
0
⇒
b
3
=
b
2
→
a
×
→
b
=
b
1
+
b
2
+
b
3
=
3
=
b
1
+
b
2
+
b
2
=
3
=
b
1
+
2
b
2
=
3
Solving then we get
b
1
=
5
3
,
b
2
=
2
3
,
b
3
=
2
3
Hence,
→
b
=
1
3
(
5
→
i
+
2
→
j
+
2
→
k
)
Hence, this is the answer.
Suggest Corrections
0
Similar questions
Q.
If
→
a
=
→
i
−
2
→
j
−
3
→
k
,
→
b
=
2
→
i
+
→
j
−
→
k
,
→
c
=
→
i
+
3
→
j
−
2
→
k
then
(
→
a
×
→
b
)
×
→
c
is
Q.
If
→
r
=
3
→
i
+
2
→
j
−
5
→
k
,
→
a
=
2
→
i
−
→
j
+
→
k
,
→
b
=
→
i
+
3
→
j
−
2
→
k
and
→
c
=
−
2
→
i
+
→
j
−
3
→
k
such that
→
r
=
λ
→
a
+
μ
→
b
+
ν
→
c
then
Q.
If
→
a
=
→
i
+
→
j
+
→
k
,
→
a
=
2
→
i
+
→
k
,
→
c
=
2
→
i
+
→
j
+
→
k
;
→
d
=
→
i
+
→
j
+
2
→
k
, then verify that
(
→
a
×
→
b
)
×
(
→
c
×
→
d
)
=
[
→
a
→
b
→
d
]
→
c
−
[
→
a
→
b
→
c
]
→
d
Q.
The unit vector which is orthogonal to the vector
→
a
=
3
→
i
+
2
→
j
+
6
→
k
and is coplanar with the vectors
→
b
=
2
→
i
+
→
j
+
→
k
and
→
c
=
→
i
−
→
j
+
→
k
is
Q.
A unit vector coplanar with
→
i
+
→
j
+
2
→
k
and
→
i
+
2
→
j
+
→
k
, and perpendicular to
→
i
+
→
j
+
→
k
, is
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