A particle moves in the $x-y$ plane under the action of a force $\overrightarrow F $ such that the value of its linear momentum $(\overrightarrow P )$ at anytime t is ${P_x} = 2\cos t,\,{p_y} = 2\sin t.$ The angle $\theta $between $\overrightarrow F $ and $\overrightarrow P $ at a given time $t$. will be $\theta =$ ........... $^o$

Obtain the scalar product of unit vectors in Cartesian co-ordinate system.

Consider two vectors ${\overrightarrow F _1} = 2\hat i + 5\hat k$ and ${\overrightarrow F _2} = 3\hat j + 4\hat k.$ The magnitude of the scalar product of these vectors is

If $\vec A,\vec B$ and $\vec C$ are vectors having a unit magnitude. If $\vec A + \vec B + \vec C = \vec 0$ then $\vec A.\vec B + \vec B.\vec C + \vec C.\vec A$ will be 

The components of $\vec a = 2\hat i + 3\hat j$ along the direction of vector $\left( {\hat i + \hat j} \right)$ is

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 $......m$.