If \frac{ay-bx}{c}=\frac{cx-az}{b}=\frac{bz-cy}{a} , then which of the following is/are correct? 1. \frac{x}{a}=\frac{y}{b} 2. \frac{x+y+z}{a+b+c}=\frac{z}{c} Select the correct answer using the code given below :

Explanation

Let the terms equal k. Multiply numerators by c, b, a respectively. Their sum is c(ay-bx) + b(cx-az) + a(bz-cy) = 0. Since sum of numerators is 0, k = 0 / (a^2+b^2+c^2) = 0. Thus, ay=bx \implies x/a=y/b, and cx=az \implies x/a=z/c. Let these equal \lambda. Then \frac{x+y+z}{a+b+c} = \frac{\lambda(a+b+c)}{a+b+c} = \lambda = \frac{z}{c}. Both are correct.

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