Question

Given, `x/(b - c ) = y/(c - a ) = z/(a - b)` , Prove that

ax+ by + cz = 0

Answer 1

Given, `x/(b - c ) = y/(c - a ) = z/(a - b)`= k (say)

 x = k (b - c ), y = k (c - a), z = k (a - b)
ax + by + cz
= ak (b - c ) + bk (c - a) + ck (a - b)
= abk - ack + bck - abk + ack - bck
= 0