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Let, aq-r=br-p=cp-q=k so, aq-r=k a=kq-r;b=kr-p;c=kp-qL.H.S.=a+b+c =kq-r+kr-p+kp-q=kq-r+r-p+p-q=k×0=0R.H.S = pa+qb+rc=pkq-r+qkr-p+rkp-q=p(kq-kr)+q(kr-kp)+r(kp-kq)=pkq-pkr+qkr-pkq+pkr-qkr=0
Therefore, a+b+c=pa+qb+ rc [Showed]
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