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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:

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As `vecx` and `vecy` are non-collinear vectors and with the given equation,
we can say that `vecx`,`vecy` and `vecx xxvecy` are linearly independent vectors.
So, their coefficients should be equal to `0`.
`20a-15b = 15b -12c = 12c-20a = 0`
`=>a/3 = b/4 , b/4 = c/5 and c/5 = a/3`
`=>a/3=b/4=c/5 `
Let `a/3=b/4=c/5 = k`
Then, `a = 3k, b = 4k, c = 5k`
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