If a,b,c are mutually perpendicular unit vectors then `|a+b+c|`=

Options

A. 1
B. 3
C. `sqrt(3)`
D. 0

Answer

C

Explanation

Since, a,b and c are mutually perpendicular unit vectors.
`rArr |a|=|b|=|c|=1`
and `ab=bc=ca=0 " "....(i)`
Now, `|a+b+c|^(2)=|a|^(2)+|b|^(2)|c|+2(ab+bc+ca)`
`=1+1+1+=` [ from Eq. (i)]
=3
`rArr |a+b+c|^(2)=3`
`rArr |a+b|c|= sqrt(3)`