Question

a +2b+3c =0 then a×b+ b×c+c×a =
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Answer 1

Step-by-step explanation:

given that a+2b+3c=0

a= -(2b+3c)

a×a= -[(2(b×a)+3(c×a)]

0= -[(2(b×a)+3(c×a)]....................(i)

Again,

2b= -(a+3c)

2b×b= -(a×b+3c×b)

0= -(a×b+3c×b)....................(ii)

from equation (i) and (ii)

-(2b×a+3c×a)+(a×b)+(3c×b)=0

3a×b-3c×a-3b×c=0

We know that,

a×b= -b×a

a×b= c×a+b×c....................(iii)

Now according to the question,

a×b+b×c+c×a=a×b+a×b=2(a×b). {from equation (iii)}

so, your answer is 2(a×b).

thanks