If $\left[\begin{array}{lll}\overline{\mathrm{a}} \times \overline{\mathrm{b}} & \overline{\mathrm{b}} \times \overline{\mathrm{c}} & \overline{\mathrm{c}} \times \overline{\mathrm{a}}\end{array}\right]=\lambda\left[\begin{array}{lll}\overline{\mathrm{a}} & \overline{\mathrm{b}} & \overline{\mathrm{c}}\end{array}\right]^2$, then $\lambda$ is equal to

If the vectors $\overline{A B}=3 \hat{i}+4 \hat{k}$ and $\overline{A C}=5 \hat{i}-2 \hat{j}+4 \hat{k}$ are the sides of the triangle $A B C$, then the length of the median, through $A$, is

If $\bar{a}$ and $\bar{b}$ are two unit vectors such that $\bar{a}+2 \bar{b}$ and $5 \overline{\mathrm{a}}-4 \overline{\mathrm{~b}}$ are perpendicular to each other, then the angle between $\bar{a}$ and $\bar{b}$ is

Let $P, Q, R$ and $S$ be the points on the plane with position vectors $-2 \hat{i}-\hat{j}, 4 \hat{i}, 3 \hat{i}+3 \hat{j}$ and $-3 \hat{i}+2 \hat{j}$ respectively. Then the quadrilateral PQRS must be a