If `veca, vecb and vecc` are vectors such that `|veca|=3,|vecb|=4 and |vec|=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

If `veca, vecb and vecc` are vectors such that `|veca|=3,|vecb|=4 and

1.	If `veca, vecb and vecc` are vectors such that `\|veca\|=3,\|vecb\|=4 and \|vec\|=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
Answer» 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`

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