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Byju's Answer
Standard XII
Physics
Position Vector
Find the valu...
Question
Find the value of m for which the vectors a = 2i + mj - 3k and b = i - 2j + k are perpendicular.
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Solution
For two vectors to be perpendicular-
a
.
b
=
0
⟹
(
2
i
+
m
j
−
3
k
)
.
(
i
−
2
j
+
k
)
=
0
⟹
2
−
2
m
−
3
=
0
⟹
m
=
−
1
2
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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.
Find a vector of magnitude
3
and perpendicular to both the vectors
b
=
2
i
−
2
j
+
k
and
c
=
2
i
+
2
j
+
3
k
.
Q.
Find a vector of magnitude
3
and perpendicular to both the vectors
→
a
=
2
¯
i
−
2
¯
j
+
¯
¯
¯
k
and
¯
¯
b
=
2
¯
i
+
2
¯
j
+
3
¯
¯
¯
k
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
^
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