Locus of the point P, for which $\overrightarrow{\mathrm{OP}}$ represents a vector with direction cosine  $\mathrm{cos\alpha }=\frac{1}{2}$ (where O is the origin) is

a ray emanating from the origin and making an angle of 60^o  with the r-axis

a disc parallel to the y-z plane with centre on the x-axis and radius equal to $\left|\overrightarrow{\mathrm{OP}}\right|\sin {60}^{\circ }$

a circle parallel to the y-z plane with centre on the x-axis

a cone concentric with the positive x-axis having vertex at the origin and the slant height equal to
the magnitude of the vector