Locus of the point P, for which `vec(OP)` represents a vector with direction cosine `cos alpha = (1)/(2)` (where O is the origin) is

Options

A. a circle parallel to the y-z plane with centre on the x-axis
B. a conic concentric with the positive x-axis having vertex at the origin and slant height equal to the magnitude of the vector
C. a ray emanating from the origin and making an angle of `60^(@) ` with the x-axis
D. a dise parallel to the y-z plane with centre on the x-axis and radius equal to `|vec(OP)| sin 60^(@)`.

Answer

B

Explanation

From the diagram, it is obvious that locus is a cone concentric with positive x-axis having vertex at the origin and the slant height equal to the magnitude of the vector.