यदि a+b+c=0, |a|=6, |b|=8 |c|=10 है तो a.b+b.c+c.a का मान है

Options

A. 100
B. `-100`
C. 200
D. `-200`

Answer

B

Explanation

हम जानते है `(a+b+c )^(2) =|a|^(2) +|b|^(2) +|c|^(2)`
`" " +2 (a.b+b.c+c.a) `
दिया है ` |a| =6,|b| =8`
`" " |c| =10` तथा `a+b+c=0`
` Arr " " 0=(6) ^(2) +(8)^(2) +(10)^(2) =2 " " (a.b+b.c+c.a)`
` rArr " " 2(a.b+b.c+c.a)=-200`
` therefore " " a.b+b.c+c.a=-100`