If `vec x` and`vec y` are two non-collinear vectors and a triangle ABC with side lengths a,b,c satisfying `(20a-15b)vec x+(15b-12c)vec y+(12c-20a)(vec x xx vec y) = vec0` . Then triangle ABC is:

Options

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

Answer

C

Explanation

Since x,y and `x xxy` are linearly independent, we have
`20a-15b-12c=12c-20a=0`
`implies (a)/(3)=(b)/(4)=(c)/(5)implies c^(2)=a^(2)+b^(2)`
Hence, `DeltaABC` is right angled.