Question

The points $A(-4,9,6)$ , $B(-1,6,6)$ and $C(0,7,10)$ forms which type of a triangle?

• A. An equilateral
• B. A right angled, isosceles
• C. A right angled
• D. A scalane

Answer 1

The correct option is B A right angled, isosceles

$\overrightarrow{AB}=3\hat{i}-3\hat{j}$
$\Rightarrow |\overrightarrow{AB}{|}^2=3^2+3^2=18$
$\overrightarrow{BC}=\hat{i}+\hat{j}+4\hat{k}$
$\Rightarrow |\overrightarrow{BC}{|}^2=4^2+1^2+1^2=18$
$\overrightarrow{CA}=-4\hat{i}+2\hat{j}-4\hat{k}$
$\Rightarrow |\overrightarrow{AC}{|}^2=4^2+2^2+4^2=36$
$A{B}^2+B{C}^2=A{C}^2$ and $|\overrightarrow{BC}|=|\overrightarrow{AB}|$. So option B is the correct option.