Q61. Consider the following two statements : Statement I : For any two non-zero complex numbers $z _ { 1 } , z _ { 2 }$, $\left( \left| z _ { 1 } \right| + \left| z _ { 2 } \right| \right) \left| \frac { z _ { 1 } } { \left| z _ { 1 } \right| } + \frac { z _ { 2 } } { \left| z _ { 2 } \right| } \right| \leq 2 \left( \left| z _ { 1 } \right| + \left| z _ { 2 } \right| \right)$, and Statement II : If $x , y , z$ are three distinct complex numbers and $\mathrm { a } , \mathrm { b } , \mathrm { c }$ are three positive real numbers such that $\frac { \mathrm { a } } { | y - z | } = \frac { \mathrm { b } } { | z - x | } = \frac { \mathrm { c } } { | x - y | }$, then $\frac { \mathrm { a } ^ { 2 } } { y - z } + \frac { \mathrm { b } ^ { 2 } } { z - x } + \frac { \mathrm { c } ^ { 2 } } { x - y } = 1$. Between the above two statements, (1) Statement I is correct but Statement II is (2) both Statement I and Statement II are correct. incorrect. (3) both Statement I and Statement II are incorrect. (4) Statement I is incorrect but Statement II is correct.
Q61. Consider the following two statements : Statement I : For any two non-zero complex numbers $z _ { 1 } , z _ { 2 }$, $\left( \left| z _ { 1 } \right| + \left| z _ { 2 } \right| \right) \left| \frac { z _ { 1 } } { \left| z _ { 1 } \right| } + \frac { z _ { 2 } } { \left| z _ { 2 } \right| } \right| \leq 2 \left( \left| z _ { 1 } \right| + \left| z _ { 2 } \right| \right)$, and\\
Statement II : If $x , y , z$ are three distinct complex numbers and $\mathrm { a } , \mathrm { b } , \mathrm { c }$ are three positive real numbers such that $\frac { \mathrm { a } } { | y - z | } = \frac { \mathrm { b } } { | z - x | } = \frac { \mathrm { c } } { | x - y | }$, then $\frac { \mathrm { a } ^ { 2 } } { y - z } + \frac { \mathrm { b } ^ { 2 } } { z - x } + \frac { \mathrm { c } ^ { 2 } } { x - y } = 1$.\\
Between the above two statements,\\
(1) Statement I is correct but Statement II is\\
(2) both Statement I and Statement II are correct. incorrect.\\
(3) both Statement I and Statement II are incorrect.\\
(4) Statement I is incorrect but Statement II is correct.