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If vec x andvec y are two non-collinear ...

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:

A

an acute angled triangle

B

an obtuse angled triangle

C

a right angled triangle

D

a scalane triangle

Text Solution

Verified by Experts

The correct Answer is:
C
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.
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