If $\vec{A} \times \vec{B} = \vec{B} \times \vec{A}$,find the angle between $\vec{A}$ and $\vec{B}$.

If $\vec{A}$ and $\vec{B}$ are two vectors satisfying the relation $\vec{A} \cdot \vec{B} = |\vec{A} \times \vec{B}|$,then the value of $|\vec{A} - \vec{B}|$ will be:

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.

If $\overrightarrow A \times \overrightarrow B = \overrightarrow C$,then which of the following statements is wrong?

Find the unit vector perpendicular to $\vec{A}$ and $\vec{B}$ where $\vec{A} = \hat{i} - 2\hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + 2\hat{j}$.

If diagonals of a parallelogram are $(5\hat i - 4\hat j + 3\hat k)$ and $(3\hat i + 2\hat j - \hat k)$,then its area is