Question

If $ax+by+cz=1,bx+cy+az=0=cx+ay+bz$, then $\left|\begin{array}{ccc}x& y& z\\ z& x& y\\ y& z& x\end{array}\right|\left|\begin{array}{ccc}a& b& c\\ c& a& b\\ b& c& a\end{array}\right|$ is equal to

• A. 0
• B. 1
• C. -1
• D. 2

Answer 1

The correct option is B 1

Given, $ax+by+cz=1,bx+cy+az=0=cx+ay+bz$.

Now $\left|\begin{array}{ccc}x& y& z\\ z& x& y\\ y& z& x\end{array}\right|\left|\begin{array}{ccc}a& b& c\\ c& a& b\\ b& c& a\end{array}\right|$

$=\left|\begin{array}{ccc}ax+by+cz& cx+ay+bz& bx+cy+az\\ bx+cy+az& ax+by+cz& cx+ay+bz\\ cx+ay+bz& bx+cy+az& ax+by+cz\end{array}\right|$

$=\left|\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right|$ [$\because ax+by+cz=1,bx+cy+az=0=cx+ay+bz$.]

$=1$