The magnitude of pairs of displacement vectors are given. Which pair of displacement vectors cannot be added to give a resultant vector of magnitude $13\, cm$?
$4 \,cm, 16 \,cm$
$20 \,cm, 7 \,cm$
$1 \,cm, 15 \,cm$
$6 \,cm, 8 \,cm$
The vector projection of a vector $3\hat i + 4\hat k$ on $Y-$axis is
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 ........... $N$