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If vecx and vecy are two non-collinear v...

If `vecx and vecy` are two non-collinear vectors and ABC is a triangle with side lengths a, b and c satisfying `(20a - 15b) vecx + ( 15b - 12c) vecy+ (12c - 20 a) (vecx xx vecy) = 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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