If $\vec{A} = 4\hat{i} + n\hat{j} - 2\hat{k}$ and $\vec{B} = 2\hat{i} + 3\hat{j} + \hat{k}$,find the value of $n$ such that $\vec{A} \perp \vec{B}$.

If two vectors $A$ and $B$ are mutually perpendicular,then the component of $A-B$ along the direction of $A+B$ is

The angle between two vectors $-2\hat{i} + 3\hat{j} + \hat{k}$ and $\hat{i} + 2\hat{j} - 4\hat{k}$ is ....... $^o$

The dot product of two mutually perpendicular vectors is:

Let $\vec A = (\hat i + \hat j)$ and $\vec B = (2\hat i - \hat j)$. The magnitude of a coplanar vector $\vec C$ such that $\vec A \cdot \vec C = \vec B \cdot \vec C = \vec A \cdot \vec B$ is given by

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: