` vec a , vec b `, and `vec c` are three vectors of equal magnitude. The angle between each pair of vectors is `pi//3` such that `| vec a+ vec b+ vec c|=sqrt6.` Then `| vec a|` is equal to a.`2` b. `-1` c. `1` d. `sqrt(6)//3`

Options

A. 2
B. `-1`
C. 1
D. `sqrt6//3`

Answer

c

Explanation

`|veca+ vecb +vecc|^(2)=6`
`or |veca|^(2)+ |vecb|^(2)+|vecc|^(2)`
`Rightarrow |veca|=|vecb|=|vecc|and veca.vecb`
` = |veca|vecb|.cos(pi/3)`
`i.e. veca.vecb= 1/2 |veca|^(2)`
` 3 |veca|^(2)+3|veca|^(2)=6`
`Rightarrow |veca|^(2)or |veca|=1`