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eliminating a, b, c from x=a/(b-c), y=b/...

eliminating a, b, c from `x=a/(b-c), y=b/(c-a) z=c/(a-b)` we get

A

`|{:(1,-x,x),(1,-y,y),(1,-z,z):}|=0`

B

`|{:(1,-x,x),(1,y,-y),(1,z,z):}|=0`

C

`|{:(1,-x,x),(y,1,-y),(-z,z,z):}|=0`

D

`|{:(1,-x,x),(y,1,-y),(z,z,z):}|=0`

Text Solution

Verified by Experts

`x=a/(b-c)rArr-a+bx-cx=0`
`y=b/(c-a)rArr-ay-b+cy=0`
`z=c/(a-b)rArraz-bz-c=0`
On eliminating a, b, c, we get
`|{:(-1,x,-x),(-y,-1,y),(z,-z,-1):}|=0`
`rArr" "(-1)^3|{:(1,-x,x),(y,1,-y),(-z,z,1):}|=0`
`rArr" "|{:(1,-x,x),(y,1,-y),(-z,z,1):}|=0`
Hence option(2) is correct.
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