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Byju's Answer
Standard XII
Mathematics
Condition for Coplanarity of Four Points
If the vector...
Question
If the vectors
→
a
=
^
i
+
^
j
+
^
k
,
→
b
=
^
i
−
^
j
+
2
^
k
,
→
c
=
x
^
i
+
(
x
−
2
)
^
j
−
^
k
are coplanar, then
x
=
A
1
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B
2
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C
0
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D
−
2
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Solution
The correct option is
C
−
2
Given equations are
→
a
=
^
i
+
^
j
+
^
k
,
→
b
=
^
i
−
^
j
+
2
^
k
,
→
c
=
x
^
i
+
(
x
−
2
)
^
j
−
→
k
These all are coplanar.
Therefore,
∣
∣ ∣
∣
1
1
1
1
−
1
2
x
x
−
2
−
1
∣
∣ ∣
∣
=
0
⇒
[
(
1
)
−
2
x
+
4
]
−
1
[
−
1
−
2
x
]
+
1
(
x
−
2
+
x
)
=
0
⇒
4
+
2
x
=
0
⇒
x
=
−
2
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0
Similar questions
Q.
If
→
a
=
^
i
+
^
j
,
→
b
=
^
j
+
^
k
,
→
c
=
α
→
a
+
β
→
b
and the vectors
^
i
−
2
^
j
+
^
k
,
3
^
i
+
2
^
j
−
^
k
,
→
c
are coplanar, then
α
β
=
Q.
Given
→
a
=
x
^
i
+
y
^
j
+
2
^
k
,
→
b
=
^
i
−
^
j
+
^
k
,
→
c
=
^
i
+
2
^
j
;
(
→
a
∧
→
b
)
=
π
2
,
→
a
.
→
c
=
4
then
Q.
If
→
a
=
^
i
+
^
j
−
^
k
,
→
b
=
−
^
i
+
2
^
j
+
2
^
k
&
→
c
=
−
^
i
+
2
^
j
−
^
k
, find a unit vectors normal to the vectors
→
a
+
→
b
and
→
b
+
→
c
.
Q.
Let,
→
a
=
^
i
+
2
^
j
+
^
k
,
→
b
=
^
i
−
^
j
+
^
k
,
→
c
=
^
i
+
^
j
−
^
k
.
A vector coplanar to
→
a
and
→
b
has a projection along
→
c
of magnitude
1
√
3
, then the vector is
Q.
If
→
a
=
2
^
i
+
^
j
+
^
k
,
→
b
=
^
i
+
2
^
j
+
2
^
k
,
→
c
=
^
i
+
^
j
+
2
^
k
and
→
a
×
(
→
b
×
→
c
)
=
(
1
+
α
)
^
i
+
β
(
1
+
α
)
^
j
+
r
(
1
+
α
)
(
1
+
β
)
^
k
, then
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