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NDA Math Vector Algebra
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© examsnet.com
Question : 55
Total: 101
If the vector
a
⋀
i
+
⋀
j
+
⋀
k
,
⋀
i
+
b
⋀
j
+
⋀
k
and
⋀
i
+
⋀
j
=
c
⋀
k
(
a
,
b
,
c
≠
1
)
are co-planar, then the value of
1
1
−
a
+
1
1
−
b
+
1
1
−
c
is equal to
[NDA II 2017]
0
1
a
+
b
+
c
abc
Validate
Solution:
|
a
1
1
1
b
1
1
1
c
|
=
0
⇒
C
2
→
C
2
−
C
1
,
C
3
→
C
3
−
C
1
|
a
1
−
a
1
−
a
1
b
−
1
0
1
0
c
−
1
|
=
0
⇒
a
(
b
−
1
)
(
c
−
1
)
−
(
1
−
a
)
(
c
−
1
)
−
(
1
−
a
)
(
b
−
1
)
=
0
Dividing by
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
,
we get
a
1
−
a
+
1
1
−
b
+
1
1
−
c
=
0
⇒
1
1
−
b
+
1
1
−
c
=
−
a
1
−
a
Adding
1
1
−
a
on both sides
1
1
−
a
+
1
1
−
b
+
1
1
−
c
=
1
© examsnet.com
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