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    				| 1. | If p, q and r are perpendicular to q + r, r + p and p + q respectively and if |p + q| = 6, |q + r| = 4sqrt(3) and |r + p| = 4, then |p + q + r| is | 
| Answer» `5sqrt(2)` `implies p^(2) +q^(2)+2p.q=36` Similarly `q^(2)+r^(2)+2q.r=48` ` andr^(2) +p^(2)+2r .p =16` Addingall weget `2( p^(2)+q^(2)r^(2)+p.q+q.r+r.p)=36+48+16` `implies 2(p^(2)+q^(2)+r^(2))=100` `[ :'p.q+q.r+r.p=0]` `implies p^(2)+q^(2)+r^(2)=50` `=|p+q+r|^(2)=50` `implies |p+q+r|=5sqrt(2)` | |