Let `veca,vecb and vecc`are vectors such that `|veca|=3,|vecb|=4and |vecc|=5, and (veca+vecb)` is perpendicular to `vecc,(vecb+vecc)` is perpendiculatr to `veca` and `(vecc+veca)` is perpendicular to `vecb`. Then find the value of `|veca+vecb+vecc|`.

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`