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Byju's Answer
Standard XII
Mathematics
Dot Product of Two Vectors
If the vector...
Question
If the vectors
→
a
=
i
−
j
+
2
k
;
→
b
=
2
i
+
4
j
+
k
and
→
c
=
2013
λ
i
+
j
−
μ
k
are mutually orthogonal then
(
λ
,
μ
)
=...
A
(
−
3
2013
;
−
2
)
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B
(
3
2013
;
−
2
)
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C
(
3
2013
;
2
)
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D
(
−
3
2013
;
2
)
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Solution
The correct option is
A
(
−
3
2013
;
−
2
)
→
a
=
i
−
^
j
+
2
k
→
b
=
2
i
−
4
j
+
k
→
c
=
2013
λ
+
j
−
μ
k
∴
→
a
&
→
c
orthogonal
⇒
→
a
.
→
c
=
0
⇒
2013
λ
−
1
−
2
μ
=
0
…
…
…
1
Also ,
→
b
&
→
c
are orthogonal
⇒
→
b
,
→
c
=
0
⇒
4026
λ
+
4
−
μ
=
0
…
…
2
Now solving these equation, we get
equation 1
×
2
equation 2
4026
λ
−
2
−
4
μ
=
0
4026
λ
+
4
−
μ
=
0
_
_
_
_
_
_
_
_
_
_
_
_
−
6
−
3
μ
=
0
3
u
=
−
6
⇒
μ
=
−
2
Also ,
2013
λ
−
1
+
4
=
0
λ
=
−
3
2013
=
−
1
671
∴
(
−
3
2013
,
−
2
)
⇒
option
(
A
)
is correct
Suggest Corrections
0
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.
→
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
Q.
If the vectors
→
a
=
^
i
−
^
j
+
2
^
k
,
→
b
=
2
^
i
+
4
^
j
+
^
k
and
→
c
=
λ
^
i
+
^
j
+
μ
^
k
are mutually orthogonal, then
(
λ
,
μ
)
=
Q.
If the vector
→
a
=
^
i
−
^
j
+
2
^
k
.
→
b
=
2
^
i
+
4
^
j
+
^
k
and
→
c
=
λ
^
i
+
^
j
+
μ
^
k
are mutually orthogonal, then
(
λ
,
μ
)
=
Q.
Let
→
a
=
2
i
−
j
+
k
,
→
b
=
^
i
+
2
^
j
−
^
k
and
→
c
=
^
i
+
^
j
−
2
^
k
be three vectors. A vector in the plane of
→
b
and
→
c
whose projection on
→
a
is of magnitude
√
2
3
is
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