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