$(\vec{a}-\vec{b}) \times(\vec{a}+\vec{b})$ is equal to :

The unit vector perpendicular to the two vectors $(2\hat{i} + 3\hat{j} + \hat{k})$ and $(\hat{i} - \hat{j} + 2\hat{k})$ is:

If the projection of $2 \hat{i} + 4 \hat{j} - 2 \hat{k}$ on $\hat{i} + 2 \hat{j} + \alpha \hat{k}$ is zero,then the value of $\alpha$ will be.

The angle between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$. The value of the triple product $\overrightarrow{A} \cdot (\overrightarrow{B} \times \overrightarrow{A})$ is

If $\overrightarrow{P} \cdot \overrightarrow{Q} = PQ,$ then the angle between $\overrightarrow{P}$ and $\overrightarrow{Q}$ is ....... $^\circ$.

Vector $\vec{F_1}$ is in the direction of the positive $X$-axis. If its cross product with another vector $\vec{F_2}$ is zero,what could be the vector $\vec{F_2}$?