If ` vec a ,\ vec b ,\ vec c` are three mutually perpendicular unit vectors, then prove that `| vec a+ vec b+ vec c|=sqrt(3)`

Options

A. 1
B. `sqrt(2)`
C. `sqrt(3)`
D. 2

Answer

C

Explanation

Given `a^(2)=b^(2)=c^(2)=1 and vec(a).vec(b)=vec(b).vec(c)=vec(c).vec(a)=0`.
`:. |vec(a)+vec(b)+vec(c)|^(2)=(vec(a)+vec(b)+vec(c)).(vec(a)+vec(b)+vec(c))`
`=vec(a).vec(a)+vec(b).vec(b)+vec(c).vec(c)+2(vec(a).vec(b)+vec(b).vec(c)+vec(c).vec(a))`
`=a^(2)+b^(2)+c^(2)+2xx0=(1+1+1+0)=3`.
Hence, `|vec(a)+vec(b)+vec(c)|=sqrt(3)`.