Two forces,each numerically equal to $10$ $dyne$,are acting as shown in the adjoining figure. The magnitude of the resultant force is ......... $dyne$.

Two equal forces ($P$ each) act at a point inclined to each other at an angle of $120^\circ$. The magnitude of their resultant is

The ratio of the maximum and minimum magnitudes of the resultant of two vectors $\vec{a}$ and $\vec{b}$ is $3 : 1$. Then $|\vec{a}|$ is equal to:

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:

The unit vector parallel to the resultant of vectors $\vec{A} = 4\hat{i} - 3\hat{j}$ and $\vec{B} = 8\hat{i} + 8\hat{j}$ is:

The resultant of $\vec{A} + \vec{B}$ is $\vec{R}_1$. On reversing the vector $\vec{B}$,the resultant becomes $\vec{R}_2$. What is the value of $R_1^2 + R_2^2$?