The two vectors have magnitudes $3$ and $5$. If angle between them is $60^o$, then the dot product of two vectors will be

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

Write the distributive law for the product of two vectors. 

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

If a vector $2\hat i + 3\hat j + 8\hat k$ is perpendicular to the vector $4\hat j - 4\hat i + \alpha \hat k$. Then the value of $\alpha $ is