If two vectors $\vec{P} = \hat{i} + 2m \hat{j} + m \hat{k}$ and $\vec{Q} = 4 \hat{i} - 2 \hat{j} + m \hat{k}$ are perpendicular to each other,then the value of $m$ will be:

The value of $(\overrightarrow A + \overrightarrow B ) \times (\overrightarrow A - \overrightarrow B )$ is

If a vector $A=2i+2j+3k$ and $B=3i+6j+nk$ are perpendicular to each other,then the value of $n$ 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 $\lambda$.

What is the angle between $\vec{A}$ and $\vec{B}$ if $\vec{A}$ and $\vec{B}$ are the adjacent sides of a parallelogram drawn from a common point and the area of the parallelogram is $\frac{AB}{2}$?

What is the angle between $(\overrightarrow P + \overrightarrow Q)$ and $(\overrightarrow P \times \overrightarrow Q)$?