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Let a,b,c be real numbers with a^(2) +...

Let a,b,c be real numbers with `a^(2) +b^(2) +c^(2)=1`. Then show that the equation
`|{:(ax-by-c,,bx+ay,,cx+a),(bx+ay,,-ax +by-c,,cy+b),(cx+a,,cy+b,,-ax-by+c):}|=0`
represents a straight line .

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