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# Given, X/(B - C ) = Y/(C - a ) = Z/(A - B) , Prove that Ax+ by + Cz = 0 - Mathematics

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#### Question

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

ax+ by + cz = 0

#### Solution

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

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Given, X/(B - C ) = Y/(C - a ) = Z/(A - B) , Prove that Ax+ by + Cz = 0 Concept: Proportions.