Byju's Answer
Standard XII
Mathematics
Linear Combination of Vectors
Let a⃗=î+ĵ ; ...
Question
Let
→
a
=
^
i
+
^
j
;
→
b
=
2
^
i
−
^
k
. Then, vector
→
r
satisfying the equations
→
r
×
→
a
=
→
b
×
→
a
and
→
r
×
→
b
=
→
a
×
→
b
is
A
^
i
−
^
j
+
3
^
k
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B
3
^
i
−
^
j
+
^
k
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C
3
^
i
+
^
j
−
^
k
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D
^
i
−
^
j
−
^
k
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Solution
The correct option is
C
3
^
i
+
^
j
−
^
k
→
r
×
→
a
=
→
b
×
→
a
and
→
r
×
→
b
=
→
a
×
→
b
⇒
→
r
×
→
a
=
−
(
→
r
×
→
b
)
⇒
→
r
×
(
→
a
+
→
b
)
=
0
→
r
=
λ
(
→
a
+
→
b
)
[
∵
angle between them is
0
]
⇒
→
r
=
λ
(
^
i
+
^
j
+
2
^
i
−
^
k
)
⇒
→
r
=
λ
(
3
^
i
+
^
j
−
^
k
)
If
λ
=
1
, then
→
r
=
3
^
i
+
^
j
−
^
k
Suggest Corrections
0
Similar questions
Q.
Let
→
a
=
ˆ
i
+
ˆ
j
,
→
b
=
2
ˆ
i
−
ˆ
k
, then vector
→
r
satisfying the equations
→
r
×
→
a
=
→
b
×
→
a
and
→
r
×
→
b
=
→
a
×
→
b
is
Q.
Let
→
a
=
^
i
+
^
j
and
→
b
=
2
^
i
−
^
k
. The point of intersection of the lines
→
r
×
→
a
=
→
b
×
→
a
and
→
r
×
→
b
=
→
a
×
→
b
is
Q.
Let
→
a
=
^
i
+
^
j
&
→
b
=
2
^
i
+
^
j
The point of intersection of the lines
→
r
×
→
a
=
→
b
×
→
a
&
→
r
×
→
b
=
→
a
×
→
b
is
Q.
If
→
a
=
^
i
−
2
^
j
+
^
k
,
→
b
=
^
j
+
^
k
, then the point of intersection of lines
→
r
×
→
a
=
→
b
×
→
a
and
→
r
×
→
b
=
→
a
×
→
b
is
Q.
Let
→
a
=
3
^
i
+
2
^
j
,
→
b
=
2
^
i
−
^
k
,
then the point of intersection of the lines
→
r
×
→
a
=
→
b
×
→
a
and
→
r
×
→
b
=
→
a
×
→
b
is
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