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Question
Mathematics
If the moduli of vectors a, b, c are 3,4,5 are respectively and a and b+c, b and c+a, c and a+b are mutually perpendicular then the modulus of a+b+c is
Q. If the moduli of vectors
a
,
b
,
c
are
3
,
4
,
5
are respectively and
a
and
b
+
c
,
b
and
c
+
a
,
c
and
a
+
b
are mutually perpendicular then the modulus of
a
+
b
+
c
is
1817
221
Vector Algebra
Report Error
A
12
B
12
C
5
2
D
50
Solution:
According to the given condition, we have
a
⋅
(
b
+
c
)
=
0
(
1
)
b
⋅
(
c
+
a
)
=
0
(
2
)
c
⋅
(
a
+
b
)
=
0
(
3
)
Now adding (1), (2) and (3), we get
2
(
a
⋅
b
+
b
⋅
c
+
c
⋅
a
)
=
0
(
∵
a
⋅
b
=
b
⋅
a
etc.
)
Hence,
∣
a
+
b
+
c
∣
2
=
a
2
+
b
2
+
c
2
+
2
(
a
⋅
b
+
b
⋅
c
+
c
⋅
a
)
=
3
2
+
4
2
+
5
2
=
9
+
16
+
25
=
50
⇒
∣
a
+
b
+
c
∣
=
50
=
5
2