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

Explanation

eqn is `(a-b)vec x + (b-c)vec y + (c-a)(vec x* vec y) = 0`

as it is equal to `0`

`:`they are linearly independent

so, `a-b=b-c=c-a=0`

`a=b=c`

`:. /_ `equilateral

option A is correct