If `veca, vecb and vecc` are vectors such that `|veca|=3,|vecb|=4 and |vecc|=5 and (veca+vecb)` is perpendicular to vecc,`(vecb+vecc) `is perpendicular to veca and `(vecc+veca)` is perpendicular to `vecb` then `|veca+vecb+vecc|=` (A) `4sqrt(3)` (B) `5sqrt(2)` (C) 2 (D) 12

Explanation

Given , `(veca+vecb)=0Rightarrowveca.vecc+vecb.vecc=0`
`(vecb+vecc).veca=0Rightarrowveca.vecb+vecc.veca=0`
`(vecc+veca).vecb=0Rightarrowvecb.vecc+veca.vecb=0`
`2(veca.vecb+vecb.vecc+vecc.veca)=0``Now, |veca+vecb+vecc|^(2)+|vecb|^(2)+|vecc|^(2)+2(veca.vecb+vecb.vecc+vecc.veca)=50`
`|veca+vecb+vecc|=5sqrt2`