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Byju's Answer
Standard XII
Mathematics
Condition for Coplanarity of Four Points
If vectors ...
Question
If vectors
→
a
=
ˆ
i
+
2
ˆ
j
−
ˆ
k
,
→
b
=
2
ˆ
i
−
ˆ
j
+
ˆ
k
and
→
c
=
λ
ˆ
i
+
ˆ
j
+
2
ˆ
k
are coplanar, then find the value of
(
λ
−
4
)
A
9
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B
10
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C
12
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D
13
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Solution
The correct option is
A
9
Vector
→
a
=
ˆ
i
+
2
ˆ
j
−
ˆ
k
,
→
b
=
2
ˆ
i
−
ˆ
j
+
ˆ
k
,
→
c
=
λ
ˆ
i
+
ˆ
j
+
2
ˆ
k
are coplanar
∴
we have
⇒
∣
∣ ∣
∣
1
2
−
1
2
−
1
1
λ
1
2
∣
∣ ∣
∣
=
0
or
λ
−
3
+
2
(
−
5
)
=
0
or
λ
=
13
Thus,
λ
−
4
=
9.
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0
Similar questions
Q.
The vectors
λ
i
+
j
+
2
k
,
i
+
λ
j
−
k
and
2
i
−
j
+
λ
k
are coplanar if
Q.
Find the value of λ so that the following vectors are coplanar:
(i)
a
→
=
i
^
-
j
^
+
k
^
,
b
→
=
2
i
^
+
j
^
-
k
^
,
c
→
=
λ
i
^
-
j
^
+
λ
k
^
(ii)
a
→
=
2
i
^
-
j
^
+
k
^
,
b
→
=
i
^
+
2
j
^
-
3
k
^
,
c
→
=
λ
i
^
+
λ
j
^
+
5
k
^
(iii)
a
→
=
i
^
+
2
j
^
-
3
k
^
,
b
→
=
3
i
^
+
λ
j
^
+
k
^
,
c
→
=
i
^
+
2
j
^
+
2
k
^
(iv)
a
→
=
i
^
+
3
j
^
,
b
→
=
5
k
^
,
c
→
=
λ
i
^
-
j
^
Q.
The vectors
λ
i
^
+
j
^
+
2
k
^
,
i
^
+
λ
j
^
-
k
^
and
2
i
^
-
j
^
+
λ
k
^
are coplanar, if λ =
(a) –2
(b) 0
(c) 1
(d) –1
Q.
If
→
a
=
i
+
j
−
k
,
→
b
=
i
−
j
+
k
,
→
c
is a vector perpendicular to
→
a
and coplanar with
→
a
and
→
b
then
→
c
=
Q.
If
→
a
=
→
i
+
2
→
j
+
→
k
,
→
b
=
2
i
−
j
+
k
,
→
c
=
j
+
2
k
and if
→
s
is any unit vector in space then the value of magnitude of
(
→
s
.
→
a
)
(
→
b
×
→
c
)
+
(
→
s
.
→
b
)
(
→
c
×
→
a
)
+
(
→
s
.
→
c
)
(
→
a
×
→
b
)
equals
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