$\left| {\,\begin{array}{*{20}{c}}a&b&c\\b&c&a\\c&a&b\end{array}\,} \right| = $
$\left| {\,\begin{array}{*{20}{c}}a&b&c\\b&c&a\\c&a&b\end{array}\,} \right| = $
- A
$3abc + {a^3} + {b^3} + {c^3}$
- B
$3abc - {a^3} - {b^3} - {c^3}$
- C
$abc - {a^3} + {b^3} + {c^3}$
- D
$abc + {a^3} - {b^3} - {c^3}$
Similar Questions
In a $\Delta ABC,$ if $\left| {\,\begin{array}{*{20}{c}}1&a&b\\1&c&a\\1&b&c\end{array}\,} \right| = 0$, then ${\sin ^2}A + {\sin ^2}B + {\sin ^2}C = $
In a $\Delta ABC,$ if $\left| {\,\begin{array}{*{20}{c}}1&a&b\\1&c&a\\1&b&c\end{array}\,} \right| = 0$, then ${\sin ^2}A + {\sin ^2}B + {\sin ^2}C = $
Which of the following is correct?
Which of the following is correct?
If the system of linear equations $x+y+3 z=0$
$x+3 y+k^{2} z=0$
$3 x+y+3 z=0$
has a non-zero solution $(x, y, z)$ for some $k \in R ,$ then $x +\left(\frac{ y }{ z }\right)$ is equal to
If the system of linear equations $x+y+3 z=0$
$x+3 y+k^{2} z=0$
$3 x+y+3 z=0$
has a non-zero solution $(x, y, z)$ for some $k \in R ,$ then $x +\left(\frac{ y }{ z }\right)$ is equal to
- [JEE MAIN 2020]
$\left| {\,\begin{array}{*{20}{c}}1&5&\pi \\{{{\log }_e}e}&5&{\sqrt 5 }\\{{{\log }_{10}}10}&5&e\end{array}\,} \right| = $
$\left| {\,\begin{array}{*{20}{c}}1&5&\pi \\{{{\log }_e}e}&5&{\sqrt 5 }\\{{{\log }_{10}}10}&5&e\end{array}\,} \right| = $
If area of triangle is $35$ $\mathrm{sq}$ $\mathrm{units}$ with vertices $(2,-6),(5,4)$ and $(\mathrm{k}, 4) .$ Then $\mathrm{k}$ is
If area of triangle is $35$ $\mathrm{sq}$ $\mathrm{units}$ with vertices $(2,-6),(5,4)$ and $(\mathrm{k}, 4) .$ Then $\mathrm{k}$ is