If ` vec xa n d vec y` are two non-collinear vectors and `A B C` isa triangle with side lengths `a ,b ,a n dc` satisfying `(20 a-15 b) vec x+(15b-12 c) vec y+(12 c-20 a)( vecx xx vec y)=0,` then triangle `A B C` is a. an acute-angled triangle b. an obtuse-angled triangle c. a right-angled triangle d. an isosceles triangle

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.