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Let the sides of a parallelogram be U=a...

Let the sides of a parallelogram be ` U=a, U=b,V=a'` and` V=b'`, where `U=lx+my+n, V=l'x+m'y+n'`. Show that the equation of the diagonal through the point of intersection of `U=a,V=a'` and `U=b,V=b'` is given by det `[[U,a,b],[V,a',b'],[1,1,1]]``=0`.

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