If $$\frac{p}{b - c} = \frac{q}{c - a} = \frac{r}{a - b}$$​, then find p + q + r.

Correct option is C

Given:

​$$\frac{p}{b - c} = \frac{q}{c - a} = \frac{r}{a - b}$$​​

Solution:

​$$\frac{p}{b - c} = \frac{q}{c - a} = \frac{r}{a - b}$$​​

Let the common ratio be ( k ). Therefore, we can write:

p = k(b - c), q = k(c - a), r = k(a - b)

Now, to find ( p + q + r ), we sum up the expressions for ( p ), ( q ), and ( r ):

p + q + r = k(b - c) + k(c - a) + k(a - b)

Simplifying this expression:

p + q + r = k[(b - c) + (c - a) + (a - b)]

Notice that the terms ( b - c ), ( c - a ), and ( a - b ) cancel each other out, so:

p + q + r = k[0] = 0

Thus, the value of p + q + r is 0.