Let a,b,c, be vectors of length 3,4,5 respectively and a be perpendicular to (b+c), b to (c+a) and c to (a+b), then the value of `(a+b+c)` is

Options

A. `2sqrt(5)`
B. `2sqrt(2)`
C. `10sqrt(5)`
D. `5sqrt(2)`

Answer

D

Explanation

`|vec(a)+vec(b)+vec(c)|=sqrt(a^(2)+b^(2)+c^(2)+2(vec(a).vec(b)+vec(b).vec(c)+vec(c).vec(a)))`
`:' vec(a).(vec(b)+vec(c))=0, vec(b).(vec(c)+vec(a))=0` & `vec(c).(vec(a)+vec(b))=0`
`rArr vec(a).vec(b)+vec(b).vec(c)+vec(c).vec(a)=0`
`rArr |vec(a)+vec(b)+vec(c)|=sqrt(a^(2)+b^(2)+c^(2))=sqrt(3^(2)+4^(2)+5^(2))=5 sqrt(2)`