Correct Answer: See Explanation

Explanation:

Let, $\frac{a}{q-r}=\frac{b}{r-p}=\frac{c}{p-q}$ = k

so, $\frac{a}{q-r}$ = k

so,

a=k(q- r); b =k(r-P) & C=k(P-q)

L.H.S = a+b+c= k(q-r) + k(r-p) + k(P-q)

=k(q-r+ r-p +P-q)=k $\times$ 0

=0R.H.S. =pa + qb + rc

=p[k(q – r)] + q [k(r-p)] + r [k(p- q)]

= p(kq – kr) + q (kr – kq) + r(kp – kq)

= pkq – pkr + qkr — pkq + pkr – qkr= 0

Therefore. a + b + c =pa + qb + rc