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EAMCET Engineering 2001 Solved Paper
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© examsnet.com
Question : 103
Total: 200
If
a
=
^
i
+
^
j
+
t
^
k
,
b
=
^
i
+
2
^
j
+
3
^
k
, then the values of 't' for which
(
a
+
b
)
and
(
a
−
b
)
are perpendicular, are
±
2
±
2
√
3
±
3
√
2
±
3
Validate
Solution:
We have,
a
+
b
=
(
^
i
+
^
j
+
t
^
k
)
+
(
^
i
+
2
^
j
+
3
^
k
)
=
2
^
i
+
3
^
j
+
(
t
+
3
)
^
k
and
a
−
b
=
(
^
i
+
^
j
+
t
^
k
)
−
(
^
i
+
2
^
j
+
3
^
k
)
=
−
^
j
+
(
t
−
3
)
^
k
Since,
(
a
+
b
)
and
(
a
−
b
)
are perpendicular to each other, then
(
a
+
b
)
⋅
(
a
−
b
)
=
0
⇒
[
2
^
i
+
3
^
j
+
(
t
+
3
)
^
k
]
⋅
[
−
^
j
+
(
t
−
3
)
^
k
]
=
0
⇒
0
−
3
+
t
2
−
9
=
0
⇒
0
t
=
±
2
√
3
© examsnet.com
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