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)`
10
15
5

Solution :`|p+q|=6implies |p+q|^(2)=36`
`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)`


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