A z 1- B z 2- C z 3 are the vertices of a right angeled isosceles triangle ABC- If - C -2- then-A- z1-z22-z1-z3z3-z2B- z1-z22-2z1-z3z3-z2C- 2z1-z22-z1-z3z3-z2D- None of these

The correct option is B Let AC = AB = r, Then AB = r√(2) z_2 z_3/z_1 z_3 = BC/AC e^iπ /2 = e^iπ / 2 z_1 z_2/z_3 z_2 = AB/BC e^iπ /4 = √(2)e^iπ / 4 and z_3 z_ ...

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Byju's Answer

Standard XI

Mathematics

Combination with Restrictions

A z 1, B z 2,...

Question

$A (z_{1}), B (z_{2}), C (z_{3})$ are the vertices of a right angeled isosceles triangle ABC. If $∠ C$ = $\frac{π}{2}$ , then:

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Solution

The correct option is B

Let AC = AB = r,

Then AB = $r \sqrt{2}$

$\frac{z_{2} - z_{3}}{z_{1} - z_{3}}$ = $\frac{B C}{A C} e^{i π / 2}$ = $e^{i π / 2}$

$\frac{z_{1} - z_{2}}{z_{3} - z_{2}}$ = $\frac{A B}{B C} e^{i π / 4}$ = $\sqrt{2} e^{i π / 4}$

and $\frac{z_{3} - z_{1}}{z_{2} - z_{1}}$ = $\frac{1}{\sqrt{2}} e^{i π / 4}$

$∴ \frac{2 (z_{3} - z_{1})}{z_{2} - z_{1}}$ = $\frac{z_{1} - z_{2}}{z_{3} - z_{2}}$

$\Rightarrow (z_{1} - z_{2})^{2}$ = $2 (z_{1} - z_{3}) (z_{3} - z_{2})$

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Similar questions

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A(z1),B(z2),C(z3) are the vertices of a right angeled isosceles triangle ABC. If ∠C = π2, then:

The correct option is B Let AC = AB = r, Then AB = r√2 z2−z3z1−z3 = BCACeiπ/2 = eiπ/2 z1−z2z3−z2 = ABBCeiπ/4 = √2eiπ/4 and z3−z1z2−z1 = 1√2eiπ/4 ∴2(z3−z1)z2−z1 = z1−z2z3−z2 ⇒(z1−z2)2 = 2(z1−z3)(z3−z2)

$A (z_{1}), B (z_{2}), C (z_{3})$ are the vertices of a right angeled isosceles triangle ABC. If $∠ C$ = $\frac{π}{2}$ , then: