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Addition of Vectors

If z1 =1 + ...

Question

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

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
$| z_{2} - z_{1} | = | 1 + i | = \sqrt{2} = a$
$| z_{3} - z_{2} | = | 1 + i | = \sqrt{2} = b$
$| z_{3} - z_{1} | = | 2 + 2 i | = 2 \sqrt{2} = c$
Clearly $a + b = c$ . Hence given 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}

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

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}

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

represent the vertices of an equilateral triangle such that

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

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

represent the vertices of an equilateral

Δ A B C

\sqrt{\frac{| z_{2} - z_{1} |^{2} + | z_{3} - z_{1} |^{2}}{| z_{2} + z_{3} - 2 z_{1} |^{2} + | z_{3} - z_{2} |^{2}}} = s i n θ

0 < θ < π

θ

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