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EAMCET Engineering 2008 Solved Paper
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© examsnet.com
Question : 118
Total: 160
If
→
a
=
^
i
+
^
j
+
^
k
,
→
b
=
^
i
−
^
j
+
^
k
,
→
c
=
^
i
+
^
j
−
^
k
and
→
d
=
^
i
−
^
j
−
^
k
, then observe the following lists
List-I
List-II
(i)
→
a
⋅
→
b
(A)
→
a
⋅
→
d
(ii)
→
→
b
⋅
→
c
(B) 3
(iii)
[
→
a
→
b
→
c
]
(C)
→
b
⋅
→
d
(iv)
→
b
×
→
c
(D)
2
^
i
−
2
^
k
(E)
2
^
j
+
2
^
k
(F) 4
The correct match of List-I to List-II
(i-C), (ii-A), (iii-B), (iv-F)
(i-C), (ii-A), (iii-F), (iv-B)
(i-A), (ii-C), (iii-B), (iv-F)
(i-A), (ii-C), (iii-F), (iv-D)
Validate
Solution:
Given vectors are
→
a
=
^
i
+
^
j
+
^
k
,
→
b
=
^
i
−
^
j
+
^
k
,
→
c
=
^
i
+
^
j
−
^
k
and
→
d
=
^
i
−
^
j
−
^
k
(i) Now,
→
a
⋅
→
a
⋅
→
b
=
(
^
i
+
^
j
+
^
k
)
⋅
(
^
i
−
^
j
+
^
k
)
=
1
−
1
+
1
=
1
→
b
⋅
→
d
=
(
^
i
−
^
j
+
^
k
)
⋅
(
^
i
−
^
j
−
^
k
)
=
1
+
1
−
1
=
1
∴
→
a
⋅
→
b
=
→
b
⋅
→
d
(ii) Now,
→
b
⋅
→
c
=
(
^
i
−
^
j
+
^
k
)
⋅
(
^
i
+
^
j
−
^
k
)
=
1
−
1
−
1
=
−
1
→
a
⋅
→
d
=
(
^
i
+
^
j
+
^
k
)
⋅
(
^
i
−
^
j
−
^
k
)
=
1
−
1
−
1
=
−
1
∴
→
b
⋅
→
c
=
→
a
⋅
→
d
(iii)
[
→
a
→
b
→
c
]
=
|
1
1
1
1
−
1
1
1
1
−
1
|
=
1
(
1
−
1
)
−
1
(
−
1
−
1
)
+
1
(
1
+
1
)
=
0
+
2
+
2
=
4
(iv)
→
b
×
→
c
=
|
^
i
^
j
^
k
1
−
1
1
1
1
−
1
|
=
^
i
(
1
−
1
)
−
^
j
(
−
1
−
1
)
+
^
k
(
1
+
1
)
=
2
^
j
+
2
^
k
Hence, option (b) is correct.
© examsnet.com
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