given a+mb+nc=0.the value of a×b+b×c+c×a is 0 then
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Answer:
We have
[(l
a
ˉ
+m
b
ˉ
+n
c
ˉ
)(l
b
ˉ
+m
c
ˉ
+n
a
ˉ
)(l
c
ˉ
+m
a
ˉ
+n
b
ˉ
)]=0
⇒
∣
∣
∣
∣
∣
∣
∣
∣
l
n
m
m
l
n
n
m
l
∣
∣
∣
∣
∣
∣
∣
∣
=0
⇒l(l
2
−mn)−m(ln−m
2
)+n(n
2
−lm)=0
⇒l
3
+m
3
+n
3
−3lmn=0
⇒(l+m+n)(l
2
+m
2
+n
2
−lm−mn−ln)=0
So, l+m+n=0
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