1.

Determine the points in i. xy-plan e ii. yz-plane and iii zx-planewhich re equidistant from the points `A(1,-1,0), B(2,1,2), a n d C(3,2,-1`)

Answer» Correct Answer - `(0,(31)/(16),(-3)/(16))`
Any point in the yz-plane is of the from P(0,y,z).
`|AP|=|BP|=|CP|hArrAP^(2)=BP^(2)=and BP^(2)=CP^(2)`
`(0-3)^(2)+(y-2)^(2)+(z+1)^(2)=(01)^(2)+(y+1)^(2)+(z-0)^(2)`
and `(0-1^(2))+(y-1)^(2)+(z-0)^(2)=(0-2)^(2)+(y-1)^(2)+(z-2)^(2)`
`rArr 3y-z-6=0 and 4y+4x-7=0`
On solving, we get `y=(31)/(16) and z=(-3)/(16)`
Hence, the requied points is `(0,(32)/(16),(-3)/(16))`


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