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KEAM 2012 Math Paper
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© examsiri.com
Question :
89 of 120
Marks:
+1
,
-0
If
−
a
=
2
⋀
i
+
2
⋀
j
−
⋀
k
,
−
b
=
α
⋀
i
+
β
⋀
j
+
2
⋀
k
and
|
−
a
+
−
b
|
=
|
−
a
−
−
b
|
,
then
α
+
β
is equal to
2
1
0
-1
-2
Validate
Solution:
Given,
a
=
2
i
+
2
j
−
k
and
b
=
α
i
+
β
j
+
2
k
∴
a
+
b
=
(
2
+
α
)
i
+
(
2
+
β
)
j
+
k
and
a
−
b
=
(
2
−
α
)
i
+
(
2
−
β
)
j
−
3
k
But it is given
|
a
+
b
|
=
|
a
−
b
|
⇒
√
(
2
+
α
)
2
+
(
2
+
β
)
2
+
1
2
=
√
(
2
−
α
)
2
+
(
2
−
β
)
2
+
9
⇒
4
+
α
2
+
4
α
+
4
+
β
2
+
4
β
+
1
=
4
+
α
2
−
4
α
+
4
+
β
2
−
4
β
+
9
⇒
8
α
+
8
β
=
8
⇒
α
+
β
=
1
© examsiri.com
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