If the square of the resultant of two forces of equal magnitude is equal to three times their product,then the angle between them is ........ $^o$.

Two forces of $10 \,N$ and $6 \,N$ act upon a body. The directions of the forces are unknown. The resultant force on the body may be .........$N$.

The resultant of two vectors $\vec{P}$ and $\vec{Q}$ is $\vec{R}$. When the direction of $\vec{Q}$ is reversed,the resultant is given by $\vec{S}$. Which one of the following is true for vectors $\vec{R}$ and $\vec{S}$?

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{R_1}$. If vector $\vec{B}$ is reversed,the resultant becomes $\vec{R_2}$. What is the value of $R_1^2 + R_2^2$?

If $\overrightarrow A = 2\widehat i + 3\widehat j + 4\widehat k$ and $\overrightarrow B = \widehat i - \widehat j + \widehat k$,find their subtraction $\overrightarrow A - \overrightarrow B$ using the algebraic method.

If $r_1=2 \hat{x}$ and $r_2=2 \hat{y}$, where $\hat{x}$ and $\hat{y}$ are unit vectors along the $X$-axis and $Y$-axis respectively, then the magnitude of $r_1+r_2$ is