If $P + Q = R$ and $|P| = |Q| = \sqrt{3}$ and $|R| = 3$,then the angle between $P$ and $Q$ is

The resultant of two vectors $\vec{P}$ and $\vec{Q}$ is $\vec{R}$. If $\vec{Q}$ is doubled,the new resultant vector is perpendicular to $\vec{P}$. What is the magnitude of $\vec{R}$?

Two forces $P$ and $Q$,of magnitude $2F$ and $3F$,respectively,are at an angle $\theta$ with each other. If the force $Q$ is doubled,then their resultant also gets doubled. Then,the angle $\theta$ is ....... $^o$

Two forces whose magnitudes are in the ratio $5:3$ are acting at a point at an angle $60^{\circ}$ simultaneously. If the resultant of the two forces is $35 \ N$,then the magnitudes of the two forces respectively are

If $\overrightarrow A = 2\hat i + \hat j$,$\overrightarrow B = 3\hat j - \hat k$,and $\overrightarrow C = 6\hat i - 2\hat k$,find the value of $\overrightarrow A - 2\overrightarrow B + 3\overrightarrow C$.

Given that $A = B = C$. If $\vec A + \vec B = \vec C$,then the angle between $\vec A$ and $\vec C$ is $\theta_1$. If $\vec A + \vec B + \vec C = 0$,then the angle between $\vec A$ and $\vec C$ is $\theta_2$. What is the relation between $\theta_1$ and $\theta_2$?