The maximum and minimum magnitude of the resultant of two given vectors are $17 $ units and $7$ unit respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is

On an open ground, a motorist follows a track that turns to his left by an angle of $60^{°}$ after every $500\; m$. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.

Given : $\vec A\, = \,2\hat i\, + \,p\hat j\, + q\hat k$ and $\vec B\, = \,5\hat i\, + \,7\hat j\, + 3\hat k,$ if $\vec A\,||\,\vec B,$ then the values of $p$ and $q$ are, respectively

Add vectors $\overrightarrow{ A }, \overrightarrow{ B }$ and $\overrightarrow{ C }$ each having magnitude of $50$ unit and inclined to the $X$-axis at angles $45^{\circ}, 135^{\circ}$ and $315^{\circ}$ respectively.

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

The vector that must be added to the vector $\hat i - 3\hat j + 2\hat k$ and $3\hat i + 6\hat j - 7\hat k$ so that the resultant vector is a unit vector along the $y-$axis is