If a, b and c represent the sides of a ∆ABC satisfying (a−b)x→+(b−c)y→+(c−a)(x→×y→)=0,where x→ and y→are two non-collinear vectors, then ∆ABC is(where x→×y→ is perpendicular to the plane of x→ and y→)
an acute-angled triangle
an obtuse-angled triangle
a right-angled triangle
a scalene triangle
As x→,y→ and x→×y→ are non-collinear vectors, vectors are linearly independent.
a−b=0=b−c=c−aor a=b=c
Therefore, the triangle is equilateral