Choose the correct answer from given four options in each of the … - Vidyadip

MCQ

Choose the correct answer from given four options in each of the Exercise:
If $\text{f(x)}=\begin{vmatrix}0&\text{x}-\text{a}&\text{x}-\text{b} \\\text{x}+\text{a} &0&\text{x}-\text{c}\\\text{x}+\text{b}&\text{x}+\text{c}&0\end{vmatrix},$ then:

A
$f(a) = 0$
B
$f(b) = 0$
✓
$f(0) = 0$
D
$f(1) = 0$

✓

Answer

Correct option: C.

$f(0) = 0$

$\text{f(x)}=\begin{vmatrix}0&\text{x}-\text{a}&\text{x}-\text{b} \\\text{x}+\text{a} &0&\text{x}-\text{c}\\\text{x}+\text{b}&\text{x}+\text{c}&0\end{vmatrix}$
$\Rightarrow\ \text{f}(0)=\begin{vmatrix}0&-\text{a}&-\text{b}\\\text{a}&0&-\text{c}\\\text{b}&\text{c}&0\end{vmatrix},$ Which is skew$-$symmetric determinant of order $3$
Hence $f(0) = 0.$

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