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Position Vector

If z_1=1...

Question

If $z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i$ , then $z_{1}, z_{2}, z_{3}$ represent the vertices of a?

A

Equilateral triangle

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B

Right angled triangle

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C

Isosceles triangle

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D

None of these

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Solution

The correct option is D None of these
$z_{3} + z_{1}$
$= 4 + 6 i$
$= 2 (2 + 3 i)$
$= 2 z_{2}$
Hence
$z_{2}$ is the mid point of $^{'} z_{3} z_{1}$
Hence all the points are collinear.

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Similar questions

z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i,

z_{1}, z_{2}

z_{3}

represent the vertices of

z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i

z_{1}, z_{2}

z_{3}

z_{1}, z_{2}, z_{3}

represent the vertices of an equilateral triangle such that

| z_{1} | = | z_{2} | = | z_{3} |

z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i, p r o v e t h a t t h e n z_{1}, z_{2} a n d z_{3}

State True and False

z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i,

z_{1}, z_{2}

z_{3}

Type 1 for true and 0 for false

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