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IIT JEE Advanced 2011 Paper 1
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© examsnet.com
Question : 55
Total: 69
The vector(s) which is/are coplanar with vectors
^
i
+
^
j
+
2
^
k
and
^
i
+
2
^
j
+
^
k
, and perpendicular to the vector
^
i
+
^
j
+
^
k
is/are
^
j
−
^
k
−
^
i
+
^
j
^
i
−
^
j
^
i
−
^
j
−
^
j
+
^
k
Validate
Solution:
Let
→
a
=
^
i
+
^
j
+
2
^
k
,
→
b
=
^
i
+
2
^
j
+
^
k
and
→
c
=
^
i
+
^
j
+
^
k
Any vector in the plane of
^
i
+
^
j
+
2
^
k
and
^
i
+
2
^
j
+
^
k
is given by
→
r
=
λ
→
a
+
µ
→
b
=
λ
(
^
i
+
^
j
+
2
^
k
)
+
µ
(
^
i
+
2
^
j
+
^
k
)
=
(
λ
+
µ
)
^
i
+
(
λ
+
2
µ
)
^
j
+
(
2
λ
+
µ
)
^
k
Also ,
→
r
.
→
c
= 0
⇒ (λ + µ) . 1 + (λ + 2µ) . 1 + (2λ + µ) . 1 = 0
⇒ 4λ + 4µ = 0
⇒ λ + µ = 0
⇒
[
→
r
→
a
→
b
]
= 0
So, vectors
^
j
−
^
k
and
−
^
j
+
^
k
satisfy this.
© examsnet.com
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