Question

The Vertices of a triangle are $A(1,0,1)B(2,-1,4)$ and $C(3,-4,-1)$ .Then The triangle is

• A. Acute Angled
• B. Obtuse Angled
• C. Equialteral
• D. Right angled

Answer 1

The correct option is D Right angled

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

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

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

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

$⟹A{B}^2+B{C}^2=A{C}^2$

So it is a right angled triangle.