Two forces of magnitude $P$ & $Q$ acting at a point have resultant $R$. The resolved  part of $R$ in the direction of $P$ is of magnitude $Q$. Angle between the forces is :

A cyclist starts from the centre $O$ of a circular park of radius $1\; km$, reaches the edge $P$ of the park, then cycles along the circumference, and returns to the centre along $QO$ as shown in Figure. If the round trip takes $10 \;min$, what is the

$(a)$ net displacement,

$(b)$ average velocity, and

$(c)$ average speed of the cyclist ?

Find unit vector perpendicular to $\vec A$ and $\vec B$ where $\vec A = \hat i - 2\hat j + \hat k$ and $\vec B = \hat i + 2\hat j$

Which of the four arrangements in the figure correctly shows the vector addition of two forces $\overrightarrow {{F_1}} $ and $\overrightarrow {{F_2}} $ to yield the third force $\overrightarrow {{F_3}} $

If two forces of equal magnitudes act simultaneously on a body in the east and the north directions then

The resultant of two vectors $\overrightarrow P $ and $\overrightarrow Q $ is $\overrightarrow R .$ If $Q$ is doubled, the new resultant is perpendicular to $P$. Then $R $ equals