The magnitude of pairs of displacement vectors are given. Which pair of displacement  vectors cannot be added to give a resultant vector of magnitude $13\, cm$?

The values of $x$ and $y$ for which vectors $\vec A = \left( {6\hat i + x\hat j - 2\hat k} \right)$ and $\vec B = \left( {5\hat i - 6\hat j - y\hat k} \right)$ may be parallel are

A motorboat is racing towards north at $25\; km / h$ and the water current in that region is $10\; km / h$ in the direction of $60^{\circ}$ east of south. Find the resultant velocity of the boat.

If two forces of $5 \,N$ each are acting along $X$ and $Y$ axes, then the magnitude and direction of resultant is

Four forces are acting at a point $P$ in equilibrium as shown in figure. The ratio of force $F_{1}$ to $F_{2}$ is $1: x$ where $x =....$

Three forces acting on a body are shown in the figure. To have the resultant force only along the $y-$ direction, the magnitude of the minimum additional force needed is  ........... $N$