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.