Let x_0 be the point of local maxima of f(x)= a ·( b × c ), where a =x i -2 j +3 k, b =-2 i +x j - k and c =7 i -2 j +x k. Then the value of a · b +…

Let $\displaystyle x_0$ be the point of local maxima of $\displaystyle f(x)=\overrightarrow{\mathbf{a}} \cdot(\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}}), \quad$ where $\displaystyle \overrightarrow{\mathrm{a}}=x \hat{i}-2 \hat{j}+3 \hat{k}, \overrightarrow{\mathrm{~b}}=-2 \hat{i}+x \hat{j}-\hat{k}$ and $\displaystyle \vec{c}=7 \hat{i}-2 \hat{j}+x \hat{k}$. Then the value of $\displaystyle \overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}}$ at $\displaystyle x=x_0$ is: