If $\alpha , \beta \, and \, \gamma$ are real numbers , then $D = \left|{\begin{array}{*{20}{c}}1&{\cos \,(\beta \, - \,\alpha )}&{\cos \,(\gamma \, - \,\alpha )}\\{\cos \,(\alpha \, - \,\beta )}&1&{\cos \,(\gamma \, - \,\beta )}\\{\cos \,(\alpha \, - \,\gamma )}&{\cos \,(\beta \, - \,\gamma )}&1 \end{array}} \right|$ =
If $\alpha , \beta \, and \, \gamma$ are real numbers , then $D = \left|{\begin{array}{*{20}{c}}1&{\cos \,(\beta \, - \,\alpha )}&{\cos \,(\gamma \, - \,\alpha )}\\{\cos \,(\alpha \, - \,\beta )}&1&{\cos \,(\gamma \, - \,\beta )}\\{\cos \,(\alpha \, - \,\gamma )}&{\cos \,(\beta \, - \,\gamma )}&1 \end{array}} \right|$ =
- A
$-1$
- B
$\cos\, \alpha \, \cos \, \beta\, \cos \, \gamma$
- C
$\cos \, \alpha + \cos \, \beta + \cos \, \gamma$
- D
$0$
Similar Questions
If $D(x) =$ $\left| {\begin{array}{*{20}{c}}{x - 1}&{{{(x - 1)}^2}}&{{x^3}}\\{x - 1}&{{x^2}}&{{{(x + 1)}^3}}\\x&{{{(x + 1)}^2}}&{{{(x + 1)}^3}}\end{array}} \right|$ then the coefficient of $x$ in $D(x)$ is
If $D(x) =$ $\left| {\begin{array}{*{20}{c}}{x - 1}&{{{(x - 1)}^2}}&{{x^3}}\\{x - 1}&{{x^2}}&{{{(x + 1)}^3}}\\x&{{{(x + 1)}^2}}&{{{(x + 1)}^3}}\end{array}} \right|$ then the coefficient of $x$ in $D(x)$ is
If $A \ne O$ and $B \ne O$ are $ n × n$ matrix such that $AB = O,$ then
If $A \ne O$ and $B \ne O$ are $ n × n$ matrix such that $AB = O,$ then
If $a\, -\, 2b + c = 1$ , then value of $\left| {\begin{array}{*{20}{c}}
{x + 1}&{x + 2}&{x + a} \\
{x + 2}&{x + 3}&{x + b} \\
{x + 3}&{x + 4}&{x + c}
\end{array}} \right|$ is
If $a\, -\, 2b + c = 1$ , then value of $\left| {\begin{array}{*{20}{c}}
{x + 1}&{x + 2}&{x + a} \\
{x + 2}&{x + 3}&{x + b} \\
{x + 3}&{x + 4}&{x + c}
\end{array}} \right|$ is
The value of $\left| {\begin{array}{*{20}{c}}
1&x&y\\
2&{\sin x + 2x}&{\sin y + 2y}\\
3&{\cos x + 3x}&{\cos y + 3y}
\end{array}} \right|$ is
The value of $\left| {\begin{array}{*{20}{c}}
1&x&y\\
2&{\sin x + 2x}&{\sin y + 2y}\\
3&{\cos x + 3x}&{\cos y + 3y}
\end{array}} \right|$ is
If the system of equations $ax + y + z = 0 , x + by + z = 0 \, \& \, x + y + cz = 0$ $(a, b, c \ne 1)$ has a non-trivial solution, then the value of $\frac{1}{{1\, - \,a}}\,\, + \,\,\frac{1}{{1\, - \,b}}\,\, + \,\,\frac{1}{{1\, - \,c}}$ is :
If the system of equations $ax + y + z = 0 , x + by + z = 0 \, \& \, x + y + cz = 0$ $(a, b, c \ne 1)$ has a non-trivial solution, then the value of $\frac{1}{{1\, - \,a}}\,\, + \,\,\frac{1}{{1\, - \,b}}\,\, + \,\,\frac{1}{{1\, - \,c}}$ is :