If $\vec{P} = (k, 2, 3)$ and $\vec{Q} = (0, 3, k)$ and $\vec{P} \perp \vec{Q}$,then what is the value of $k$?

The vector product of two vectors $2\hat{i} + \hat{j}$ and $\hat{i} + 2\hat{j}$ is:

Two position vectors are given by $\overrightarrow{r_1} = (1, 1, 1)$ and $\overrightarrow{r_2} = (1, -1, 1)$. Find the unit vector in the direction of $\overrightarrow{r_1} \times \overrightarrow{r_2}$.

$\hat{i} \cdot (\hat{j} \times \hat{k}) + \hat{j} \cdot (\hat{k} \times \hat{i}) + \hat{k} \cdot (\hat{i} \times \hat{j}) = $

If $\theta$ is the angle between vectors $\vec{A}$ and $\vec{B}$,then what is the value of the product $(\vec{B} \times \vec{A}) \cdot \vec{A}$?

Show that the scalar product of two vectors obeys the distributive law.