If $\overrightarrow{ A }=(2 \hat{ i }+3 \hat{ j }-\hat{ k }) \;m$ and $\overrightarrow{ B }=(\hat{ i }+2 \hat{ j }+2 \hat{ k })\; m$. The magnitude of component of vector $\overrightarrow{ A }$ along vector $\vec{B}$ will be $......m$.

The angle between $(\overrightarrow A - \overrightarrow B )$ and $(\overrightarrow A \times \overrightarrow B )$ is $(\overrightarrow{ A } \neq \overrightarrow{ B })$

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

Which of the following is the unit vector perpendicular to $\overrightarrow A $ and $\overrightarrow B $

Find the angle between two vectors with the help of scalar product.

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