Question

The points $\left(0,2,0\right), \left(\sqrt{3} , 1 , 0 \right)$ and $ \left(\frac{1}{\sqrt{3}} , 1, \frac{2\sqrt{2}}{\sqrt{3}}\right)$ are the vertices of

• A. a scalene triangle
• B. an equilateral triangle
• C. an isosceles triangle
• D. none of these.

Answer 1

Answer: (B)

If the points are $A (0, 2, 0), B ( \sqrt{3} , 1, 0)$ and $C\left(\frac{1}{\sqrt{3}} , 1 , \frac{2\sqrt{2}}{\sqrt{3}}\right) $ , then $\left|AB\right|=\left|BC\right|=\left|CA\right|$
$= 2$ so that the triangle $ABC$ is equilateral.