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Question
Mathematics
If a, b, c are three vectors such that |a|=3,|b|=4, |c|=5 and a, b, c are perpendicular to b+c, c+a, a +b respectively, then |a+b+c|=
Q. If
a
,
b
,
c
are three vectors such that
∣
a
∣
=
3
,
∣
b
∣
=
4
,
∣
c
∣
=
5
and
a
,
b
,
c
are perpendicular to
b
+
c
,
c
+
a
,
a
+
b
respectively, then
∣
a
+
b
+
c
∣
=
2565
197
Vector Algebra
Report Error
A
6
2
B
4
2
C
3
2
D
5
2
Solution:
∵
a
⊥
(
b
+
c
)
∴
a
⋅
(
b
+
c
)
=
0
⇒
a
⋅
b
+
a
⋅
c
=
0
(
1
)
Similarly
b
⊥
(
c
+
a
)
⇒
b
⋅
c
+
b
⋅
a
=
0
(
2
)
and
c
⊥
(
a
+
b
)
=
0
⇒
c
⋅
a
+
c
⋅
b
=
0
(
3
)
Adding (1), (2), (3), we get
2
(
a
⋅
b
+
b
⋅
c
+
c
⋅
a
)
=
0
Now,
(
a
+
b
+
c
)
2
=
a
2
+
b
2
+
c
2
+
2
(
a
⋅
b
+
b
⋅
c
+
c
⋅
a
)
=
∣
a
∣
2
+
∣
b
∣
2
+
∣
c
/
2
+
0
=
(
3
)
2
+
(
4
)
2
+
(
c
)
2
=
50
Hence,
∣
a
+
b
+
c
∣
=
5
2