Question

Assertion(A): $(1,0)(\frac{1}{2},\frac{\sqrt{3}}{2})(\frac{1}{2},\frac{\sqrt{3}}{2})$ forms an equilateral triangle
Reason (R): The cube roots of unity taken as vertices of a triangle then the triangle is an equilateral triangle.

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is not the correct explanation of A
• C. A is false, R is true.
• D. A is true R is false.

Answer 1

Answer: (C)

A is false, R is true.

For an equilateral triangle, the argument between two sides must be ${60}^0$, and their modulus must be equal.
Here, the modulus is not equal and hence it cannot be an equilateral triangle.
However, cube roots of unity form an equilateral triangle among them.