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Byju's Answer
Standard XII
Mathematics
Condition for Two Lines to Be Perpendicular
If A= 1,2,3...
Question
If
A
=
(
1
,
2
,
3
)
,
B
=
(
−
2
,
4
,
λ
)
and
∠
A
O
B
=
π
/
2
where
O
is the origin then
λ
is
A
6
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B
−
6
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C
0
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D
−
2
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Solution
The correct option is
D
−
2
The vector OA is given by
i
+
2
j
+
3
k
and vector OB is given by
−
2
i
+
4
j
+
λ
k
.
Since the angle between them is
90
0
their dot product is zero.
Thus, we have
−
2
+
8
+
3
λ
=
0
⇒
λ
=
−
2
.
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0
Similar questions
Q.
The value of
λ
for which the equation
x
+
y
−
3
=
0
,
(
1
+
λ
)
x
+
(
2
+
λ
)
y
−
8
=
0
,
x
−
(
1
+
λ
)
y
+
(
2
+
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)
=
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are consistent is
Q.
The value of
λ
for which the equations
x
+
y
−
3
=
0
,
(
1
+
λ
)
x
+
(
2
+
λ
)
y
−
8
=
0
,
x
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(
1
−
λ
)
y
+
(
2
+
λ
)
=
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are consistent is
Q.
If
z
be a complex number such that
|
z
−
2
|
=
2
|
z
−
1
|
, then
|
z
|
2
=
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R
e
(
z
)
, where
λ
is-
Q.
If
∣
∣ ∣ ∣
∣
a
2
+
λ
2
a
b
+
c
λ
c
a
−
b
λ
a
b
−
c
λ
b
2
+
λ
2
b
c
+
a
λ
c
a
+
b
λ
b
c
−
a
λ
c
2
+
λ
2
∣
∣ ∣ ∣
∣
∣
∣ ∣
∣
λ
c
−
b
−
c
λ
a
b
−
a
λ
∣
∣ ∣
∣
=
(
1
+
a
2
+
b
2
+
c
2
)
3
, then the value of
λ
is
Q.
The values of
λ
for which the system of equations
(
λ
+
5
)
x
+
(
λ
−
4
)
y
+
z
=
0
(
λ
−
2
)
x
+
(
λ
+
3
)
y
+
z
=
0
λ
x
+
λ
y
+
z
=
0
has a non-trivial solution is (are)
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