Let x,y,z in C satisfy |x| = 1, |y-6-8...

Let `x,y,z in` C satisfy `|x| = 1, |y-6-8i| = 3` and `|z + 1-7i| = 5` respectively, then the minimum value of `|x-z| + |y-z|` is equal to

`1`

`2`

`5`

`6`

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Verified by Experts

The correct Answer is:

To find minimum valume of `|x-z| + |y-z|`, we know that
` |z_(1)+z_(2)| le |z_(1)|+ |z_(2)|" " AA z_(1),z_(2) in C`
`therefore |x-z|+|y-z|ge |(x-z)+(-y+z)|`
`implies E ge |x-y|`
Also, equality holds when x,y,z are collinear points.
`therefore |x-y|_(min) =c_(1)c_(2)-(r_(1)+r_(2))`
`10-(1+3)=10-4=6`

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