If `vecx and vecy ` are two non-collinear vectors and a, b and c represent the sides of a `Delta ABC` satisfying `(a-b)vec x + (b-c)vecy+ (c-a)(vecxxx vecy) =0`, then `Delta ABC` is (where `vecx xx vecy` is perpendicular to the plane of `vecx and vecy`)

Options

A. an acute-angled triangle
B. an obtuse-angled triangle
C. a right-angled triangle
D. a scalene triangle

Answer

A

Explanation

As `vecx, vecy and vecx xx vecy` are non-collinear vectors, vectors are linearly independent. Hence,
`" "a - b=0 = b -c =c -a `
or `a = b = c`
Therefore, the triangle is equilateral.