If x→ and y→ are two non-collinear vectors and a,b,c represent the sides of a △ABC satisfying (a−b)x→+(b−c)y→+(c−a)(x→×y→)=0, then ΔABC is:
an acute angle triangle
an obtuse angle triangle
a right angle triangle
a scalene triangle
As x→,y→ and x→×y→ are non-coplanar vectors ⇒ linearly independent.
Therefore, a−b=0=b−c=c−a
⇒ a=b=c⇒Δ is equilateral.