The angle between two vectors $4\hat{i} + 3\hat{j} + \hat{k}$ and $-3\hat{i} + 2\hat{j} + 6\hat{k}$ is ....... $^o$

Three vectors $\vec{A}, \vec{B}$ and $\vec{C}$ are such that $\vec{A} \cdot \vec{B} = 0$ and $\vec{A} \cdot \vec{C} = 0$. Then $\vec{A}$ is parallel to:

The angle between the two vectors $(2\hat{i} + 3\hat{j} + \hat{k})$ and $(-3\hat{i} + 6\hat{k})$ is ...... $^\circ$.

$A$ vector $\vec{A}$ points vertically upward and $\vec{B}$ points towards north. The vector product $\vec{A} \times \vec{B}$ is

If the vector $2\hat{i} + 3\hat{j} - \hat{k}$ is perpendicular to the vector $-4\hat{i} - 6\hat{j} + \lambda\hat{k}$,find the value of $\lambda$.

The diagonals of a parallelogram are $2\,\hat{i}$ and $2\,\hat{j}$. What is the area of the parallelogram in square units?