The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{C}$. If the magnitude of $\vec{B}$ is doubled,the new resultant vector becomes perpendicular to $\vec{A}$. Then,the magnitude of $\vec{C}$ 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:

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 the direction of a vector $\overrightarrow{A}$ is reversed,find $\Delta \overrightarrow{A}$ and $|\Delta \overrightarrow{A}|$.

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

$A$ vector $P$ directed along the $X$-axis is added to vector $Q$ which has a magnitude of $10 \ m$. The resultant vector is directed along the $Y$-axis,with a magnitude that is $2$ times that of $P$. The magnitude of $P$ is