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JEE Advanced 2018 Paper 1
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© examsnet.com
Question : 48
Total: 54
Let
→
a
and
→
b
be two unit vectors such that
→
a
→
b
=
0
.For some
x
,
y
∊
ℝ
,
let
→
c
=
x
→
a
+
y
→
b
+
(
→
a
×
→
b
)
.If
|
→
c
|
=
2
and the vector
→
c
is inclined at the same angle
α
to both
→
a
and
→
b
, then the value of
8
c
o
s
2
α
is
Your Answer:
Validate
Solution:
→
c
=
x
→
a
+
y
→
b
+
→
a
×
→
b
→
c
.
→
a
=
x
and
x
=
2
c
o
s
α
→
c
.
→
a
=
y
and
y
=
2
c
o
s
α
Also
|
→
a
×
→
b
|
=
1
∴
→
c
=
2
c
o
s
(
→
a
+
→
b
)
+
→
a
×
→
b
→
c
2
=
4
c
o
s
2
α
(
→
a
+
→
b
)
2
+
(
→
a
+
→
b
)
2
+
2
c
o
s
α
(
→
a
+
→
b
)
.
(
→
a
×
→
b
)
4
=
8
c
o
s
2
α
+
1
8
c
o
s
2
α
=
3
© examsnet.com
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