The complex numbers z1-z2 and z3 satisfying z1-z3-z2-z3-1-3i-2 are the vertices of a triangle- which is

The correct option is C equilateralGiven: arg (z_1 z_3z_2 z_3)= π3 And, |z_1 z_3z_2 z_3|=|1 √(3)i2 |=1 Therefore, |z_1 z_3|=|z_2 z_3| Thus, two sid ...

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Standard XII

Mathematics

Double Ordinate

The complex n...

Question

The complex numbers $z_{1}, z_{2}$ and $z_{3}$ satisfying $\frac{z_{1} - z_{3}}{z_{2} - z_{3}} = \frac{1 - \sqrt{3} i}{2}$ are the vertices of a triangle, which is

of area

= 0

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right-angled isoceles

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equilateral

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obtuse-angled isoceles

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Solution

The correct option is C equilateral
Given:
$a r g (\frac{z_{1} - z_{3}}{z_{2} - z_{3}}) = \frac{- π}{3}$
And,
$∣ ∣ ∣ \frac{z_{1} - z_{3}}{z_{2} - z_{3}} ∣ ∣ ∣ = ∣ ∣ ∣ \frac{1 - \sqrt{3} i}{2} ∣ ∣ ∣ = 1$
Therefore,
$| z_{1} - z_{3} | = | z_{2} - z_{3} |$
Thus, two sides are equal in the given triangle and one of the included angle is $\frac{π}{3}$ .
Therefore, it is an equilateral triangle.
Hence, option C is correct.

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The complex numbers z1,z2 and z3 satisfying z1−z3z2−z3=1−√3i2 are the vertices of a triangle, which is

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