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

Let $\overrightarrow A = \hat iA\,\cos \theta + \hat jA\,\sin \theta $ be any vector. Another vector $\overrightarrow B $ which is normal to $\overrightarrow A$ is

Find the angle between two vectors $\vec A = 2\hat i + \hat j - \hat k$ and $\vec B = \hat i - \hat k$ ....... $^o$

If $\vec{A}$ and $\vec{B}$ are two vectors satisfying the relation $\vec{A} . \vec{B}=[\vec{A} \times \vec{B}]$. Then the value of $[\vec{A}-\vec{B}]$. will be :

$\overrightarrow A $ and $\overrightarrow B $ are two vectors given by $\overrightarrow A  = 2\widehat i + 3\widehat j$ and $\overrightarrow B  = \widehat i + \widehat j$. The magnitude of  the component (projection) of $\overrightarrow A$ on $\overrightarrow  B$ is

A vector $\overrightarrow A $ points vertically upward and $\overrightarrow B $points towards north. The vector product $\overrightarrow A \times \overrightarrow B $ is