Two forces,$F_1$ and $F_2$,are acting on a body. One force is double that of the other force and the resultant is equal to the greater force. Then the angle between the two forces is

$A$ 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

The displacement of a particle from a point having position vector $2 \hat{i} + 4 \hat{j}$ to another point having position vector $5 \hat{i} + 1 \hat{j}$ is ........ units.

If the sum of two unit vectors is a unit vector,then the magnitude of their difference is

The magnitudes of two vectors are $8$ units and $6$ units respectively. Find the magnitude of the resultant vector if the angle between these two vectors is $(i) \theta = 0^{\circ}$,$(ii) \theta = 180^{\circ}$,$(iii) \theta = 90^{\circ}$,and $(iv) \theta = 120^{\circ}$.

Vectors $\vec{A}$ and $\vec{B}$ make angles of $20^\circ$ and $110^\circ$ with the $X$-axis respectively. The magnitudes of these vectors are $5 \, m$ and $12 \, m$ respectively. Find the angle made by the resultant vector with the $X$-axis.