Question

The points A$(-2,3,5),B(1,2,3)andC(7,0,-1)$ are _____

• A. Collinear
• B. Vertex of equilateral triangle
• C. vertex of right angle triangle
• D. vertex of right angled isosceles triangle

Answer 1

The correct option is A

Collinear

Let A$\equiv (-2,3,5)$

B$\equiv (1,2,3)$

C$\equiv (7,0,-1)$

AB = $\sqrt{(1+2{)}^2+(2-3{)}^2+(3-5{)}^2}$ = $\sqrt{9+1+4}$ = $\sqrt{14}$

BC = $\sqrt{(7-1{)}^2+(0-2{)}^2+(-1-3{)}^2}$ = $\sqrt{36+4+16}$ = 2$\sqrt{14}$

AC = $\sqrt{(7+2{)}^2+(0-3{)}^2+(-1-5{)}^2}$ = $\sqrt{81+9+36}$ = 3$\sqrt{14}$

Thus AB+BC=Ac

Hence points A,B,C are collinear and B lies between A & C