Question 53

If $$\frac{a}{q-r}=\frac{b}{r-p}=\frac{c}{p-q}$$, find the value of pa+qp+rc is

Solution

Let $$\dfrac{a}{q-r} = k$$

$$\dfrac{pa}{pq-pr} = k$$

$$pa = k(pq-pr) = kpq-kpr$$

$$\dfrac{b}{r-p} = k$$

$$qb = k(qr-pq) = kqr-kpq$$

$$\dfrac{c}{p-q} = k$$

$$rc = k(rp-rq) = kpr-kqr$$

pa+qb+rc = kpq-kpr+kqr-kpq+kpr-kqr = 0

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