Two forces $F_1 = 3 \ N$ at $0^o$ and $F_2 = 5 \ N$ at $60^o$ act on a body. Then a single force that would balance the two forces must have a magnitude of .......... $N$

If the resultant vector of vectors $\vec{A} = 4\hat{i} + 3\hat{j} + 6\hat{k}$ and $\vec{B} = -\hat{i} + 3\hat{j} - 8\hat{k}$ is parallel to a unit vector,then $\vec{R}$ is:

Two forces,each of magnitude $F$,have a resultant of the same magnitude $F$. The angle between the two forces is....... $^o$

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 $\vec{R}$?

Give the equations to find the magnitude and direction of the resultant vector of two vectors $\vec{A}$ and $\vec{B}$ that are inclined at an angle $\theta$ to each other.

$A$ vector $P$ has $X$ and $Y$ components of magnitude $2$ units and $4$ units respectively. $A$ vector $Q$ along the negative $X$-axis has a magnitude of $6$ units. The vector $(Q - P)$ will be