If a/(q -r) = b/(r-p) = c/(p-q), then p...

If ` a/(q -r) = b/(r-p) = c/(p-q)`, then prove that ` a + b + c = 0 =pa+ qb + rc`.

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`a/(q-r) = b/(r-p) = /(p-q) = k " (let)" [k ne 0]`
` :. A = k ( q - r), b = k (r -p) , c = k (p -q)`
` :. A + b + c = k (q - r) + k (r - p) + k (p -q)`
` = k (q - r + r - p + p - q) =k xx 0 = 0`.
Again , ` pa + qb + rc = p.k (q - r) + q.k (r - p) + r.k (p-q)`
` = k (pq - pr+qr - pq + pr -qr)`
` = k xx 0 = 0`.
` :. a + b + c = 0 = pa + qb + rc `

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