Question

The triangle formed by the vertices $A(1,0,1)B(2,-1,4)$ and $C(3,-4,-1)$ is

• A. Equilateral Triangle
• B. Isoceles Triangle
• C. Right angled Triangle
• D. Obtuse angled Triangle

Answer 1

The correct option is C Right angled Triangle

Guven$A(1,0,1)B(2,-1,4)$ and $C(3,-4,-1)$

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

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

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

$⟹(\sqrt{11}{)}^2+(\sqrt{24}{)}^2=11+24=35=(\sqrt{35}{)}^2$

$⟹A{B}^2+A{C}^2=B{C}^2$

So it is a right angled triangle.