$\bar{a}=\hat{i}-\hat{j}, \bar{b}=\hat{j}-\hat{k}, \bar{c}=\hat{k}-\hat{i}$ then a unit vector $\bar{d}$ such that $\overline{\mathrm{a}} \cdot \overline{\mathrm{d}}=0=[\overline{\mathrm{b}} \overline{\mathrm{c}} \overline{\mathrm{d}}]$ is

In $\triangle A B C$, with usual notations, if $\mathrm{a}^4+\mathrm{b}^4+\mathrm{c}^4-2 \mathrm{a}^2 \mathrm{c}^2-2 \mathrm{c}^2 \mathrm{~b}^2=0$, then $\angle \mathrm{C}=\ldots$

If the planes $\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-\lambda \hat{\mathrm{j}}+\hat{\mathrm{k}})=3$ and $\overline{\mathrm{r}} \cdot(4 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\mu \hat{\mathrm{k}})=5$ are parallel, then $\lambda+\mu=$

If $x$ is real, then the difference between the greatest and least values of $\frac{x^2-x+1}{x^2+x+1}$ is