If ` vec a , vec b ,` and `vec c` are unit vectors such that ` vec a+ vec b+ vec c=0,` then find the value of ` vec a.vec b+ vec b.vec c+ vecc.vec adot`

Options

A. `(1)/(2)`
B. `(-1)/(2)`
C. `(3)/(2)`
D. `(-3)/(2)`

Answer

D

Explanation

`(vec(a)+vec(b)+vec(c)).(vec(a)+vec(b)+vec(c))=0`
`rArr|vec(a)|^(2)+|vec(b)|^(2)+|vec(c)|^(2)+2(vec(a).vec(b)+vec(b).vec(c)+vec(c).vec(a))=0`
`rArr(vec(a).vec(b)+vec(b).vec(c)+vec(c).vec(a))=(-3)/(2)" " [:'|vec(a)|=|vec(b)|=|vec(c)|=1]`.