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Byju's Answer
Standard XII
Mathematics
Applications of Dot Product
If the vector...
Question
If the vectors
2
i
+
λ
j
−
k
and
2
i
−
2
j
+
2
k
are perpendicular to each other then find
λ
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Solution
If they are perpendicular
2
×
2
+
λ
×
−
2
+
(
−
1
)
×
2
=
0
2
λ
=
2
λ
=
1
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2
Similar questions
Q.
For what value of λ are the vectors
a
→
=
2
i
^
+
λ
j
^
+
k
^
and
b
→
=
i
^
-
2
j
^
+
3
k
^
perpendicular to each other?
Q.
Write the value of λ so that the vectors
a
→
=
2
i
^
+
λ
j
^
+
k
^
and
b
→
=
i
^
-
2
j
^
+
3
k
^
are perpendicular to each other.
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.
Find the value of λ if the vectors
2
i
^
+
λ
j
^
+
3
k
^
and
3
i
^
+
2
j
^
-
4
k
^
are perpendicular to each other.
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