The points $(5,-4,5),(-3,-3,2)$ and $(-1,-6,8)$ form ......
The points $(5,-4,5),(-3,-3,2)$ and $(-1,-6,8)$ form ......
an isosceles triangle
an equilateral triangle
a right-angled isosceles triangle
a right-angled triangle
Solution
Given points $A(5,-4,5), B(-3,-3,2)$ and
$
\begin{aligned}
& C(-1,-6,8) \\
& \therefore \quad A B=\sqrt{64+1+9}=\sqrt{74} \\
& B C=\sqrt{4+9+36}=7 \\
& \text { and } \quad C A=\sqrt{36+4+9}=7
\end{aligned}
$
$\because$ Length of sides $B C$ and $C A$ are equal, but $B C^2+C A^2 \neq A B^2$
$\therefore \triangle A B C$ is an isosceles triangle