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

Options

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

Answer

C

Explanation

Since `vecx , vecy and vecx xx vecy` are linearly independent, we have
`20a - 15b = 15b - 12c =12c - 20 a =0`
`rArr (a)/(3) = (b)/(4) = (c )/(5)`
`rArr c^(2) = a^(2) + b^(2)`
Hence, `Delta ABC` is right angled.