Question

The triangle with vertices $A(1,0,1),B(2,-1,4)andC(3,-4,-1),$ is right-angled.

• A. True
• B. False

Answer 1

The correct option is A True

The Vertices are $A(1,0,1)B(2,-1,4)$ and $C(3,-4,-1)$

$AB=\sqrt{(1-2{)}^2+(0+1{)}^2+(1-4{)}^2}=\sqrt{1+1+9}=\sqrt{11}$

$BC=\sqrt{(3-2{)}^2+(-4+1{)}^2+(-1-4{)}^2}=\sqrt{1+9+25}=\sqrt{35}$

$AC=\sqrt{(1-3{)}^2+(0+4{)}^2+(1+1{)}^2}=\sqrt{4+16+4}=\sqrt{24}$

$⟹A{B}^2+A{C}^2=B{C}^2$

So it is a right-angled triangle.