If $x = cy + bz,\,\,y = az + cx,\,\,z = bx + ay$ (where $x, y, z $ are not all zero) have a solution other than $x = 0$, $y = 0$, $z = 0$ then $a, b$ and $ c $ are connected by the relation
If $x = cy + bz,\,\,y = az + cx,\,\,z = bx + ay$ (where $x, y, z $ are not all zero) have a solution other than $x = 0$, $y = 0$, $z = 0$ then $a, b$ and $ c $ are connected by the relation
- [IIT 1978]
- A
${a^2} + {b^2} + {c^2} + 3abc = 0$
- B
${a^2} + {b^2} + {c^2} + 2abc = 0$
- C
${a^2} + {b^2} + {c^2} + 2abc = 1$
- D
${a^2} + {b^2} + {c^2} - bc - ca - ab = 1$
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- [JEE MAIN 2021]
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