If $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$ are unit vectors such that $|\overline{\mathrm{a}}+\overline{\mathrm{b}}|=\sqrt{3}$, then the angle between $\bar{a}$ and $\bar{b}$ is

Three vectors $\hat{\mathrm{i}}-\hat{\mathrm{k}}, \lambda \hat{\mathrm{i}}+\hat{\mathrm{j}}+(1-\lambda) \hat{\mathrm{k}}$ and $\mu \hat{\mathrm{i}}+\lambda \hat{\mathrm{j}}+(1+\lambda-\mu) \hat{\mathrm{k}}$ represents coterminous edges of a parallelopiped, then the volume of the parallelopiped depends on.

The line of intersection of the planes $\bar{r} \cdot(3 \hat{i}-\hat{j}+\hat{k})=1 \quad$ and $\quad \bar{r} \cdot(\hat{i}+4 \hat{j}-2 \hat{k})=2 \quad$ is parallel to the vector

The lines $\overline{\mathrm{r}}=\overline{\mathrm{a}}+\lambda(\overline{\mathrm{b}} \times \overline{\mathrm{c}})$ and $\overline{\mathrm{r}}=\overline{\mathrm{c}}+\lambda(\overline{\mathrm{a}} \times \overline{\mathrm{b}})$ will intersect if