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
A
`1`
B
`2`
C
`5`
D
`6`
Text Solution
Verified by Experts
The correct Answer is:
D
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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