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Byju's Answer
Standard XII
Mathematics
Applications of Dot Product
Let a⃗, b⃗,...
Question
Let
→
a
,
→
b
,
→
c
be three vectors such that
|
→
a
|
=
3
,
|
→
b
|
=
4
,
|
→
c
|
=
5
and each one of the perpendicular to the sum of the other two, find
|
→
a
+
→
b
+
→
c
|
.
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Solution
(
→
a
)
=
3
,
(
→
b
)
=
4
,
→
k
=
5
→
a
⋅
→
b
,
→
b
⋅
→
c
a
n
d
→
a
⋅
→
c
a
r
e
p
e
r
p
e
n
d
i
c
u
l
a
r
∴
→
a
⋅
→
b
=
→
b
⋅
→
c
=
→
c
⋅
→
a
=
0
T
h
e
n
,
∣
∣
→
a
+
→
b
+
→
c
∣
∣
2
=
|
→
a
|
2
+
∣
∣
→
b
∣
∣
2
+
|
→
c
|
2
+
2
(
→
a
⋅
→
b
+
→
b
⋅
→
c
+
→
c
⋅
→
a
)
⇒
∣
∣
→
a
+
→
b
+
→
c
∣
∣
=
√
3
2
+
4
2
‘
+
5
2
+
0
⇒
5
√
2
U
n
i
t
s
A
n
s
.
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0
Similar questions
Q.
Let
→
a
,
→
b
and
→
c
be three vectors such that
|
→
a
|
=
3
∣
∣
→
b
∣
∣
=
4
|
→
c
|
=
5
and each one of them being perpendicular to the sum of the other two find
∣
∣
→
a
+
→
b
+
→
c
∣
∣
.
Q.
→
a
;
→
b
;
→
c
are three vectors so that each one is perpendicular to the sum of the other two and also
|
→
a
|
=
40
;
|
→
b
|
=
20
;
|
→
c
|
=
4
then
|
→
a
+
→
b
+
→
c
|
+
.......
Q.
Let
→
a
,
→
b
and
→
c
be three vectors such that
|
→
a
|
=
√
3
,
|
→
b
|
=
5
,
→
b
.
→
c
=
10
and the angle between
→
b
and
→
c
is
π
3
.
If
→
a
is perpendicular to vector
→
b
×
→
c
, then
|
→
a
×
(
→
b
×
→
c
)
|
is equal to
Q.
If
→
a
,
→
b
,
→
c
are three vectors such that
→
a
×
→
b
=
→
c
,
→
b
×
→
c
=
→
a
,
→
c
×
→
a
=
→
b
then prove that
|
→
a
|
=
|
→
b
|
=
|
→
c
|
Q.
Let
→
A
=
→
b
×
→
c
,
→
B
=
→
c
×
→
a
,
→
C
=
→
a
×
→
b
, then the vectors
→
A
×
(
→
B
×
→
C
)
,
→
B
×
(
→
C
×
→
A
)
, and
→
C
×
(
→
A
×
→
B
)
are
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