If $A,B,C$ are three points in the Argand plane representing the complex numbers ${z_1},{z_2},{z_3}$ such that ${z_1} = \frac{{{\rm{\lambda }}{z_2} + {z_3}}}{{{\rm{\lambda }} + 1}},$ where ${\rm{\lambda }} \in {\rm{R}},$ then the distance of $A$ from the line $BC$ is

$\frac{{\rm{\lambda }}}{{{\rm{\lambda }} + 1}}$

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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A,B,C

are three points in the Argand plane representing the complex numbers

{z_1},{z_2},{z_3}

such that

{z_1} = \frac{{\mathrm{\lambda }{z_2} + {z_3}}}{{\mathrm{\lambda } + 1}},

where

\mathrm{\lambda } \in \mathrm{R},

then the distance of

A

from the line

BC

View answer and explanation

Correct option: D

Option D (0) is correct because the given condition implies that point A lies on the line segment BC, hence the distance of A from the line BC is zero.

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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