The value of = | ccc 0 & & - - & 0 & & - & 0 | is - Vidyadip

MCQ

The value of $\Delta=\left|\begin{array}{ccc}0 & \sin \alpha & -\cos \alpha \\ -\sin \alpha & 0 & \sin \beta \\ \cos \alpha & -\sin \beta & 0\end{array}\right|$ is

✓
$0$
B
$1$
C
$2$
D
$3$

✓

Answer

Correct option: A.

$0$

Expanding along $R_1$, we get
$ \Delta=0-\sin \alpha(0-\sin \beta \cos \alpha)-\cos \alpha(\sin \alpha \sin \beta-0)$
$=\sin \alpha \sin \beta \cos \alpha-\cos \alpha \sin \alpha \sin \beta=0$

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