Question

STATEMENT 1: In a $\Delta ABC,a,b,c$ denotes lengths of the sides and $\left|\begin{array}{ccc}a& b& c\\ b& c& a\\ c& a& b\end{array}\right|=0$ then the triangle is equilateral triangle.
STATEMENT 2: Sum of three non-negative numbers $=0\Rightarrow$ each number is zero.

• A. Statement-1 is true, Statement-2 is true, Statement-2 is correct explanation of Statement- 1
• B. Statement-1 is true, Statement-2 is true, Statement-2 is not correct explanation for Statement-1
• C. Statement-1 is true, Statement-2 is false
• D. Statement-1 is false, Statement-2 is true

Answer 1

The correct option is A Statement-1 is true, Statement-2 is true, Statement-2 is correct explanation of Statement- 1

$\left|\begin{array}{ccc}a& b& c\\ b& c& a\\ c& a& b\end{array}\right|$
$=0$
$R_1\to R_1+R_2+R_3$
$\left|\begin{array}{ccc}(a+b+c)& (a+b+c)& (a+b+c)\\ b& c& a\\ c& a& b\end{array}\right|$
$=0$
$\left|\begin{array}{ccc}1& 1& 1\\ b& c& a\\ c& a& b\end{array}\right|$
$=0$
$a+b+c=0,b,c,a>0$
$\therefore a=b=c=0$