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Byju's Answer
Standard XII
Mathematics
Linear Dependence and Independence of Vectors
If a=i+j+k,...
Question
If
a
=
i
+
j
+
k
,
b
=
4
i
+
3
j
+
4
k
and
c
=
i
+
α
j
+
β
k
are linearly dependent vectors and
|
c
|
=
√
3
, then
A
α
=
1
,
β
=
−
1
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B
α
=
1
,
β
=
±
1
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C
α
=
−
1
,
β
=
±
1
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D
α
=
±
1
,
β
=
1
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Solution
The correct option is
D
α
=
±
1
,
β
=
1
Since
a
,
b
,
c
are linearly dependent.
[
a
b
c
]
=
0
⇒
∣
∣ ∣
∣
1
1
1
4
3
4
1
α
β
∣
∣ ∣
∣
=
0
⇒
∣
∣ ∣
∣
1
0
0
4
−
1
0
1
α
−
1
β
−
1
∣
∣ ∣
∣
=
0
⇒
−
(
β
−
1
)
=
0
⇒
β
=
1
Also,
|
c
|
=
√
2
⇒
1
+
α
2
+
β
2
=
3
⇒
α
2
=
1
⇒
α
=
±
1
Suggest Corrections
1
Similar questions
Q.
If
a
=
i
+
j
+
k
,
b
=
4
i
+
3
j
+
4
k
and
c
=
i
+
α
j
+
β
k
are linearly dependent vectors and
|
c
|
=
√
3
, then the values of
α
and
β
are respectively.
Q.
If
→
a
=
^
i
+
^
j
+
^
k
,
^
b
=
4
^
i
+
3
^
j
+
4
^
k
and
→
c
=
^
i
+
α
^
j
+
β
^
k
are linearly dependent vectors and
|
→
c
|
=
√
3
,
then
Q.
If
→
a
= i + j + k ,
→
b
= 4i + 3j + 4k ,
→
c
= i +
α
i +
β
k are linearly dependent and
|
c
|
=
√
3
then
Q.
Diameter of the circle given by
|
(
z
−
α
)
/
(
z
−
β
)
|
=
k
,
k
≠
1
, where
α
,
β
are fixed points and
z
is varying point in argand plane is
Q.
If
a
=
^
i
+
^
j
+
^
k
,
b
=
4
^
i
+
3
^
j
+
4
^
k
and
c
=
^
i
+
α
^
j
+
β
^
k
are linearly dependent vectors and
|
c
|
=
√
3
, then the value of
α
and
β
are respectively
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