Match the following
COLUMN - I COLUMN - II
A) If z₁, z₂, z₃ are vertices
of an equilateral triangle then p) ${(z_{1} - z_{2})}^{2} + 3 {(z_{3} - z_{2})}^{2} = 0$
B) If z₁, z₂, z₃ are vertices of A, B, C of an isosceles right angled triangle
respectively with right angle at C,
then q) ${(z_{2} - z_{3})}^{2} = 3 (z_{1} - z_{2}) (z_{3} - z_{1})$
C) If z₁, z₂, z₃ are vertices of A, B, C of an isosceles triangle respectively and angles B & C are
each equal to $\frac{π}{6}$ then
r) ${(z_{1} - z_{2})}^{2} = 2 (z_{1} - z_{3}) (z_{3} - z_{2})$
D) If z₁, z₂, z₃ are vertices of A, B, C respectively
of a triangle ABC in which $∠ A = \frac{π}{6}, ∠ B = \frac{π}{2}, ∠ C = \frac{π}{3}, then$ s) ${(z_{1} - z_{2})}^{2} + {(z_{2} - z_{3})}^{2} + {(z_{3} - z_{1})}^{2} = 0$
(A) (B) (C) (D)
1) s r q p
2) r q s q
3) p s r r
4) q p p s

Question

Infinity Learn · Accepted Answer

Detailed Solution

	COLUMN - I		COLUMN - II
A)	If z₁, z₂, z₃ are vertices of an equilateral triangle then	p)	${(z_{1} - z_{2})}^{2} + 3 {(z_{3} - z_{2})}^{2} = 0$
B)	If z₁, z₂, z₃ are vertices of A, B, C of an isosceles right angled triangle respectively with right angle at C, then	q)	${(z_{2} - z_{3})}^{2} = 3 (z_{1} - z_{2}) (z_{3} - z_{1})$
C)	If z₁, z₂, z₃ are vertices of A, B, C of an isosceles triangle respectively and angles B & C are each equal to $\frac{π}{6}$ then	r)	${(z_{1} - z_{2})}^{2} = 2 (z_{1} - z_{3}) (z_{3} - z_{2})$
D)	If z₁, z₂, z₃ are vertices of A, B, C respectively of a triangle ABC in which $∠ A = \frac{π}{6}, ∠ B = \frac{π}{2}, ∠ C = \frac{π}{3}, then$	s)	${(z_{1} - z_{2})}^{2} + {(z_{2} - z_{3})}^{2} + {(z_{3} - z_{1})}^{2} = 0$