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Byju's Answer
Standard XII
Mathematics
Algebra of Complex Numbers
If p #160; ...
Question
If
p
→
=
5
i
^
+
λ
j
^
-
3
k
^
and
q
→
=
i
^
+
3
j
^
-
5
k
^
,
then find the value of λ, so that
p
→
+
q
→
and
p
→
-
q
→
are perpendicular vectors.
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Solution
Given that
p
→
=
5
i
^
+
λ
j
^
-
3
k
^
a
n
d
q
→
=
i
^
+
3
j
^
-
5
k
^
p
→
+
q
→
=
5
i
^
+
λ
j
^
-
3
k
^
+
i
^
+
3
j
^
-
5
k
^
=
6
i
^
+
λ
+
3
j
^
-
8
k
^
p
→
-
q
→
=
5
i
^
+
λ
j
^
-
3
k
^
-
i
^
+
3
j
^
-
5
k
^
=
4
i
^
+
λ
-
3
j
^
+
2
k
^
Given that
p
→
+
q
→
is orthogonal to
p
→
-
q
→
.
⇒
p
→
+
q
→
.
p
→
-
q
→
=
0
⇒
6
i
^
+
λ
+
3
j
^
-
8
k
^
.
4
i
^
+
λ
-
3
j
^
+
2
k
^
=
0
⇒
24
+
λ
2
-
9
-
16
=
0
⇒
λ
2
=
1
∴
λ
=
±
1
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0
Similar questions
Q.
If
p
→
=
5
i
^
+
λ
j
^
-
3
k
^
and
q
→
=
i
^
+
3
j
^
-
5
k
^
,
then find the value of λ, so that
p
→
+
q
→
and
p
→
-
q
→
are perpendicular vectors.
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.
If the volume of parallelopiped whose coterminous edges are
¯
¯
¯
a
=
3
¯
i
−
¯
j
+
4
¯
¯
¯
k
,
¯
¯
b
=
2
¯
i
+
3
¯
j
−
¯
¯
¯
k
and
¯
¯
c
=
−
5
¯
i
+
2
¯
j
+
3
¯
¯
¯
k
is three times the volume of parallelopiped whose coterminous edges are
¯
¯
¯
p
=
¯
i
+
¯
j
+
3
¯
¯
¯
k
,
¯
¯
¯
q
=
¯
i
−
2
¯
j
+
λ
¯
¯
¯
k
and
¯
¯
¯
r
=
2
¯
i
+
3
¯
j
then the value of
λ
is
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.
If
a
→
=
5
i
^
-
j
^
-
3
k
^
and
b
→
=
i
^
+
3
j
^
-
5
k
^
,
then show that the vectors
a
→
+
b
→
and
a
→
-
b
→
are orthogonal.
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