JEE Advance - Mathematics (2001 - No. 15)

Let $$a, b, c$$ be real numbers with $${a^2} + {b^2} + {c^2} = 1.$$ Show that

the equation $$\left| {\matrix{ {ax - by - c} & {bx + ay} & {cx + a} \cr {bx + ay} & { - ax + by - c} & {cy + b} \cr {cx + a} & {cy + b} & { - ax - by + c} \cr } } \right| = 0$$


represents a straight line.
The determinant is equal to 0.
The determinant represents a straight line.
The determinant represents a circle.
The determinant represents a parabola.
The determinant is a constant value.

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