Maximum and minimum magnitudes of the resultant of two vectors of magnitudes $P$ and $Q$ are in the ratio $3:1.$ Which of the following relations is true?

The unit vector parallel to the resultant of the vectors $\vec A = 4\hat i + 3\hat j + 6\hat k$ and $\vec B = - \hat i + 3\hat j - 8\hat k$ is

Two vectors $\vec A$ and $\vec B$ have magnitudes $2$ and $1$ respectively. If the angle between $\vec A$ and $\vec B$ is $60^{\circ}$,then which of the following vectors may be equal to $\frac{\vec A}{2} - \vec B$?

The sum of the magnitudes of two forces acting at a point is $16 \,N$. If their resultant is normal to the smaller force and has a magnitude of $8 \,N$, then the forces are:

The sum of the magnitudes of two vectors acting at a point is $18$ and the magnitude of their resultant is $12$. If the resultant is at $90^{\circ}$ with the vector of smaller magnitude,then the magnitudes of the vectors are

While travelling from one station to another,a car travels $75 \, km$ North,$60 \, km$ North-east,and $20 \, km$ East. The minimum distance between the two stations is.......$km$