$A$ man walks $20\,m$ at an angle $60^{\circ}$ north of east. How far towards the east has he travelled?

$A$ vector is represented by $3\,\hat i + \hat j + 2\,\hat k$. Its length in the $XY$ plane is

Three vectors $\overrightarrow{OP}, \overrightarrow{OQ}$ and $\overrightarrow{OR}$ each of magnitude $A$ are acting as shown in the figure. The resultant of the three vectors is $A \sqrt{x}$. The value of $x$ is:

What is the maximum number of components a vector can have when resolved in a plane?

Two forces act on point $A$ along the sides $AC$ and $AB$ of a right-angled triangle $ABC$ (where $\angle A = 90^{\circ}$). The magnitudes of these forces are inversely proportional to the lengths of the sides $AC$ and $AB$ respectively. If $F_1 = 1/AC$ and $F_2 = 1/AB$,then the resultant of these forces is proportional to:

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