Question

If planes $x-cy-bz=0,cx-y+az=0$ and $bx+ay-z=0$ pass through a straight line then $a^2+b^2+c^2=$

• A. $1-abc$
• B. $abc-1$
• C. $1-2abc$
• D. $2abc-1$

Answer 1

The correct option is C $1-2abc$

Since,the planes passes through a straight line means the given planes are Concurrent
$\left|\begin{array}{ccc}1& -c& -b\\ c& -1& a\\ b& a& -1\end{array}\right|=0$
$\Rightarrow 1-a^2-c^2-abc-abc-b^2=0\Rightarrow a^2+b^2+c^2+2abc=1\Rightarrow a^2+b^2+c^2=1-2abc$
Therefore Answer is $C$