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JEE Main 9 Jan 2020 Shift 1 Solved Paper
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© examsnet.com
Question : 74
Total: 75
If the vectors,
→
p
=
(
a
+
1
)
^
i
+
a
^
j
+
a
^
k
,
→
q
=
a
^
i
+
(
a
+
1
)
^
j
+
a
^
k
and
→
r
=
a
^
i
+
a
^
j
+
(
a
+
1
)
^
k
(a ∈ R) are coplanar and
3
(
→
p
.
→
q
)
2
−
λ
|
→
r
×
→
q
|
2
=
0
, then the value of λ is ------.
Your Answer:
Validate
Solution:
→
p
=
(
a
+
1
)
^
i
+
a
^
j
+
a
^
k
,
→
q
=
a
^
i
+
(
a
+
1
)
^
j
+
a
^
k
and
→
r
=
a
^
i
+
a
^
j
+
(
a
+
1
)
^
k
∵
→
p
,
→
q
,
→
r
are coplanar
⇒
[
→
p
→
q
→
r
]
=
0
⇒
|
a
+
1
a
a
a
a
+
1
a
a
a
a
+
1
|
=
0
⇒
3
a
+
1
=
0
⇒
a
=
−
1
3
→
p
.
→
q
=
−
1
3
,
→
r
.
→
q
=
−
1
3
|
→
r
|
2
=
|
→
q
|
2
=
2
3
3
(
→
p
.
→
q
)
2
−
λ
|
→
r
×
→
q
|
2
=
0
⇒
λ
=
3
(
→
p
.
→
q
)
2
|
→
r
×
→
q
|
2
=
3
(
→
p
.
→
q
)
2
|
→
r
|
2
|
→
q
|
2
−
(
→
r
.
→
q
)
=
1.00
© examsnet.com
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