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Combination Based on Geometry

If 2z1-3z2-...

Question

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

A

three vertices of a rhombus

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B

three vertices of a triangle

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C

three points are collinear

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D

None of these

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Solution

The correct option is A three points are collinear
$2 z_{1} - 3 z_{2} - z_{3} = 0$
$2 z_{1} = 3 z_{2} + z_{3}$
$z_{1} = \frac{3 z_{2} + z_{3}}{2}$
Therefore,
$z_{1}, z_{2}, z_{3}$ are collinear.
Hence, option 'C' is correct.

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