The resultant of two forces $3P$ and $2P$ is $R$. If the first force is doubled,then the resultant is also doubled. The angle between the two forces is ........... $^o$.

$A$ particle is simultaneously acted upon by two forces equal to $4\, N$ and $3\, N$. The net force on the particle is

Two forces $P + Q$ and $P - Q$ make an angle $2 \alpha$ with each other,and their resultant makes an angle $\theta$ with the bisector of the angle between them. Then:

The $x$ and $y$ components of vector $\vec{P}$ have magnitudes $1$ and $3$,and the $x$ and $y$ components of the resultant of $\vec{P}$ and $\vec{Q}$ have magnitudes $5$ and $6$ respectively. What is the magnitude of $\vec{Q}$?

Explain the parallelogram method for vector addition. Also,explain how this is comparable to the triangle method.

The resultant of two vectors at an angle $150^{\circ}$ is $10$ units and is perpendicular to one vector. The magnitude of the smaller vector is ....... units