The vectors $5i + 8j$ and $2i + 7j$ are added. The magnitude of the sum of these vector is

If $\vec{P}+\vec{Q}=\overrightarrow{0}$, then which of the following is necessarily true?

The resultant of $\vec A$ and $\vec B$ makes an angle $\alpha $ with $\vec A$ and $\beta $ with $\vec B$,

The sum of three forces ${\vec F_1} = 100\,N,{\vec F_2} = 80\,N$ and ${\vec F_3} = 60\,N$ acting on a particle is zero. The angle between $\vec F_1$ and $\vec F_2$ is nearly .......... $^o$

The resultant of two vectors at an angle $150^{\circ}$ is $10$ units and is perpendicular to one vector. The magnitude of the smaller vector is ....... units

A body is moving under the action of two forces ${\vec F_1} = 2\hat i - 5\hat j\,;\,{\vec F_2} = 3\hat i - 4\hat j$. Its velocity will become uniform under an additional third force ${\vec F_3}$ given by