If A ≡ z1, B ≡ z2, C ≡ z3 be the vertices of triangle A B C. And origin O is the orthocentre of the triangle A B C then

Question

If A ≡ z1, B ≡ z2, C ≡ z3 be the vertices of triangle A B C. And origin O is the orthocentre of the triangle A B C then (A) z1 barz2+ barz1 z2=z2 barz3+ barz2 z3=z3 barz1+ barz3 z1 (B) |z1|=|z2|=|z3| (C) z1 z2 z3=1 (D) None of these

Tardigrade Admin · Accepted Answer

Correct answer is (a) z1 barz2+ barz1 z2=z2 barz3+ barz2 z3=z3 barz1+ barz3 z1

Q. If $A \equiv z_{1}, B \equiv z_{2}, C \equiv z_{3}$ be the vertices of $△ A BC$ . And origin $O$ is the orthocentre of the $△ A BC$ then

$z_{1} \overset{z}{ˉ}_{2} + \overset{z}{ˉ}_{1} z_{2} = z_{2} \overset{z}{ˉ}_{3} + \overset{z}{ˉ}_{2} z_{3} = z_{3} \overset{z}{ˉ}_{1} + \overset{z}{ˉ}_{3} z_{1}$

$∣ z_{1} ∣ = ∣ z_{2} ∣ = ∣ z_{3} ∣$

$z_{1} z_{2} z_{3} = 1$

None of these

Correct answer is (a) $z_{1} \overset{z}{ˉ}_{2} + \overset{z}{ˉ}_{1} z_{2} = z_{2} \overset{z}{ˉ}_{3} + \overset{z}{ˉ}_{2} z_{3} = z_{3} \overset{z}{ˉ}_{1} + \overset{z}{ˉ}_{3} z_{1}$

Q. If A≡z1​,B≡z2​,C≡z3​ be the vertices of △ABC. And origin O is the orthocentre of the △ABC then

z1​zˉ2​+zˉ1​z2​=z2​zˉ3​+zˉ2​z3​=z3​zˉ1​+zˉ3​z1​

∣z1​∣=∣z2​∣=∣z3​∣

z1​z2​z3​=1