If a, b, c are sides of a scalene triangle,th | vedclass

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(B) Let $\Delta = \left| \begin{array}{ccc} a & b & c \ b & c & a \ c & a & b \end{array} ight|$.Applying $R_1 	o R_1 + R_2 + R_3$,we get:$\Delta

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(B) Let $\Delta = \left| \begin{array}{ccc} a & b & c \ b & c & a \ c & a & b \end{array} ight|$.Applying $R_1 	o R_1 + R_2 + R_3$,we get:$\Delta = (a+b+c) \left| \begin{array}{ccc} 1 & 1 & 1 \ b & c & a \ c & a & b \end{array} ight|$.Expanding the determinant:$\Delta = (a+b+c) [1(bc - a^2) - 1(b^2 - ac) + 1(ab - c^2)]$$\Delta = (a+b+c) (bc + ac + ab - a^2 - b^2 - c^2)$.Multiplying and dividing by $2$:$\Delta = -\frac{1}{2}(a+b+c) [2a^2 + 2b^2 + 2c^2 - 2ab - 2bc - 2ca]$$\Delta = -\frac{1}{2}(a+b+c) [(a-b)^2 + (b-c)^2 + (c-a)^2]$.Since $a, b, c$ are sides of a scalene triangle,$a, b, c > 0$ and $a 
eq b 
eq c$.Thus,$(a+b+c) > 0$ and $[(a-b)^2 + (b-c)^2 + (c-a)^2] > 0$.Therefore,$\Delta < 0$.

If $a, b, c$ are sides of a scalene triangle,then the value of $\left| \begin{array}{ccc} a & b & c \\ b & c & a \\ c & a & b \end{array} \right|$ is

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