The angle between vectors $(\vec{M} \times \vec{N})$ and $(\vec{N} \times \vec{M})$ is ................ (in $^{\circ}$)

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

If the vectors $\vec P = a\hat i + a\hat j + 3\hat k$ and $\vec Q = a\hat i - 2\hat j - \hat k$ are perpendicular to each other,then the positive value of $a$ is

The edges of a parallelepiped are represented by the vectors $\hat{i} + 2\hat{j}$,$4\hat{j}$,and $\hat{j} + 3\hat{k}$. Find its volume.

Write the necessary condition for the scalar product of two mutually perpendicular vectors.

Let $|\vec{A}_1| = 3$,$|\vec{A}_2| = 5$,and $|\vec{A}_1 + \vec{A}_2| = 5$. The value of $(2\vec{A}_1 + 3\vec{A}_2) \cdot (3\vec{A}_1 - 2\vec{A}_2)$ is (in $.5$)