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AP EAMCET Engineering 2018 Apr 22 Shift 2 Paper
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© examsnet.com
Question : 33
Total: 160
If
a
and
b
are two unit vectors such that
c
=
(
a
×
c
)
+
b
, then the maximum value of
[
a
b
c
]
is
1
1
2
3
2
2
Validate
Solution:
c
=
(
a
×
c
)
+
b
|
c
|
2
=
|
a
+
c
|
2
+
|
b
|
2
+
2
(
a
×
c
)
.
b
[
a
b
c
]
=
1
2
[
1
−
|
c
|
2
cos
2
θ
]
Now,
c
.
(
a
.
c
)
=
(
a
×
c
)
2
+
b
.
(
a
×
c
)
[
a
b
c
]
=
|
c
|
2
sin
2
θ
=
sin
2
θ
cos
2
θ
+
2
sin
2
θ
=
1
cosec
2
θ
+
1
For maximum value of
[
a
b
c
]
,
cosec
2
θ
=
1
.
So,
[
a
b
c
]
max
=
1
1
+
1
=
1
2
© examsnet.com
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