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Byju's Answer
Standard XII
Mathematics
Condition for Two Lines to be on the Same Plane
a⃗ =∧ i -2∧ j...
Question
→
a
=
∧
i
−
2
∧
j
+
3
∧
k
,
→
b
=
−
2
∧
i
+
3
∧
j
−
4
∧
k
and
→
c
=
∧
i
−
3
∧
j
+
λ
∧
k
are co-planar if
λ
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Solution
we have to given
→
a
=
^
i
−
2
^
j
+
3
^
k
,
→
b
=
−
2
^
i
+
3
^
j
−
4
^
k
and
→
c
=
^
i
−
3
^
j
+
λ
^
k
Three vectors are co-planer if
[
→
a
→
b
→
c
]
=
0
----
(
i
)
Therefore,
[
→
a
→
b
→
c
]
=
∣
∣ ∣
∣
1
−
2
3
−
2
3
−
4
1
−
3
λ
∣
∣ ∣
∣
from
(
i
)
and expanding along
R
1
0
=
1
(
3
λ
−
12
)
−
(
−
2
)
(
−
2
λ
+
4
)
+
3
(
6
−
3
)
3
λ
−
12
+
8
−
4
λ
+
9
=
0
−
λ
+
5
=
0
λ
=
5
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Similar questions
Q.
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
)
Q.
If
→
a
=
i
+
2
j
+
k
,
→
b
=
i
−
j
+
k
and
→
c
=
i
+
j
−
k
. A vector in the plane of
→
a
and
→
b
whose projection on
→
c
is
1
/
√
3
, is
Q.
Let
→
a
=
i
+
2
j
+
k
,
→
b
=
i
−
j
+
k
and
→
c
=
i
+
j
−
k
, a vector in the plane
→
a
and
→
b
whose projection on
→
c
is
1
√
3
is _____
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 + j + k ,
→
b
= 4i + 3j + 4k ,
→
c
= i +
α
i +
β
k are linearly dependent and
|
c
|
=
√
3
then
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