If ` vec xa n d vec y` are two non-collinear vectors and a, b, and c represent the sides of a ` A B C` satisfying `(a-b) vec x+(b-c) vec y+(c-a)( vec x xx vec y)=0,` then ` A B C` is (where ` vec xxx vec y` is perpendicular to the plane of `xa n dy` ) a. an acute-angled triangle b. an obtuse-angled triangle c. a right-angled triangle d. a scalene triangle

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.