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Byju's Answer
Standard IX
Mathematics
Representation of Vectors
ntThree vecto...
Question
ntThree vectors a, b, c are such that a+b+c=0. If a=3,b=4,c=5, show that ab=bc=ca=-25n
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Similar questions
Q.
If
a
,
b
,
c
are real numbers such that
a
b
a
+
b
=
1
3
,
b
c
b
+
c
=
1
4
and
c
a
c
+
a
=
1
5
, then the value of
a
b
c
a
b
+
b
c
+
c
a
is
Q.
Show that :
∣
∣ ∣ ∣
∣
b
c
−
a
2
c
a
−
b
2
a
b
−
c
2
−
b
c
+
c
a
+
c
b
b
c
−
c
a
+
a
b
b
c
+
c
a
−
a
b
(
a
+
b
)
(
a
+
c
)
(
b
+
c
)
(
b
+
a
)
(
c
+
a
)
(
c
+
b
)
∣
∣ ∣ ∣
∣
=
3
(
b
−
c
)
(
c
−
a
)
(
a
−
b
)
(
a
+
b
+
c
)
(
b
c
+
c
a
+
a
b
)
.
Q.
If a, b, c are rational numbers such that
a
2
+
b
2
+
c
2
−
a
b
−
b
c
−
c
a
=
0
,
prove that
a
=
b
=
c
.
Q.
If
¯
¯
¯
a
,
¯
¯
b
,
¯
¯
c
are three vectors such that
|
¯
¯
¯
a
|
=
1
,
|
b
|
=
2
,
|
c
|
=
3
and
¯
¯
¯
a
¯
¯
b
=
¯
¯
b
¯
¯
c
=
¯
¯
c
⋅
¯
¯
¯
a
=
0
. Then
[
¯
¯
¯
a
¯
¯
b
→
c
]
=
Q.
If
a
b
+
c
=
b
c
+
a
=
c
a
+
b
, prove that
a
(
b
−
c
)
+
b
(
c
−
a
)
+
c
(
a
−
b
)
=
0
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