If , find the value of ax + by + cz.

Mathematics

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⇒ $\dfrac{x}{b - c} = \dfrac{y}{c - a} = \dfrac{z}{a - b}$ = m (let)

⇒ x = m(b - c)

⇒ y = m(c - a)

⇒ z = m(a - b)

Substituting value of x, y and z in ax + by + cz, we get :

⇒ a[m(b - c)] + b[m(c - a)] + c[m(a - b)]

⇒ a[mb - mc] + b[mc - ma] + c[ma - mb]

⇒ amb - amc + bmc - bma + cma - cmb

⇒ 0.

Hence, ax + by + cz = 0.

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