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Area Method to Find Condition for Co-Linearity

If 2z1 - 3z...

Question

If $2 z_{1} - 3 z_{2} + z_{3} = 0$ then $z_{1}, z_{2}, z_{3}$ are represented by

A

three vertices of a triangle

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B

three vertices of a rhombus

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C

three collinear points

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D

none of these

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Solution

The correct option is B three collinear points
Given, $2 z_{1} + z_{3} = 3 z_{2}$
$z_{2} = \frac{2 z_{1} + z_{3}}{2 + 1}$
So $z_{2}$ divide the line joining the point $z_{1}, z_{3}$ are in the ratio of 1 : 2.
So $z_{1}, z_{2}, z_{3}$ are colliner.

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0 < θ < π

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Area Method to Find Condition for Co-Linearity

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