The ratio of maximum and minimum magnitudes of the resultant of two vector $\vec a$ and $\vec b$ is $3 : 1$. Now $| \vec a |$ is equal to
$| \vec b |$
$2| \vec b |$
$3| \vec b |$
$4| \vec b |$
Two forces acting on point $A$ along their side and having magnitude reciprocal to length of side then resultant of these forces will be proportional to
If $\vec A$ and $\vec B$ are two non-zero vectors such that $\left| {\vec A + \vec B} \right| = \frac{{\left| {\vec A - \vec B} \right|}}{2}$ and $\left| {\vec A} \right| = 2\left| {\vec B} \right|$ then the angle between $\vec A$ and $\vec B$ is
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
The vectors $5i + 8j$ and $2i + 7j$ are added. The magnitude of the sum of these vector is